Differences Between Delirium, Depression Dementia, Delusions, Alzheimer's

Lots of D's to differentiate.
Alzheimer's disease is one form or type of dementia. The most common form or type of dementia. Dementia is the loss of cognitive ability. A global generic term. There are many other causes of dementia besides the most common Alzheimer's disease. Lewy body dementia, Vascular dementia, traumatic brain injury induced, to name a couple.
The different forms of dementia may look slightly different in their clinical symptoms and presentation and progression.
Dementia is a chronic problem it is typically slow and often progressive.
Delirium is way different. A delirium is an acute confusional state, or an encephalopathy. It generally comes in pretty quickly, hence the term "acute". There is always a cause for delirium. It may be a metabolic problem, eg. not enough oxygen to the brain or too much carbon dioxide, such as someone with really bad lung or heart disease, or a metabolic problem, someones sodium for example is too high or low, or a toxicity, such as illicit drugs or drug withdrawal, alcohol withdrawal is a common cause. A severe infection with for example a high fever is another cause.
Delirium is always a medical emergency. It can have a high death rate up to 25% or more, especially if not treated.  Usually it is very treatable, the issue is diagnosing it and finding the cause. 
Often it is mistaken for a psychiatric problem. A common symptom is visual hallucinations, seeing things, example bugs crawling on the wall. Sometimes there are tactile hallucinations, feeling things that are not there, such as bugs crawling on one's skin. These kind of hallucinations usually again indicate an "organic" or medical reason and problem.
A person can get extremely agitated in delirium, bizarre, violent aggressive behavior, it often gets worse at night and fluctuates over the course of the day. Sundowning is a term that has been associated with delirium.
A person with dementia can get agitated and worse at night. We also associate the term sundowning with Alzheimer's also, or more agitation at night. Wandering about etc.
A person with dementia can also develop a delirium on top of that. A common cause for example is a person that has Alzheimer's dementia and develops a urinary tract infection, or a metabolic imbalance.
That is where it gets more difficult to diagnose. Usually there is more of an acute change in the persons behavior, a significant worsening or change over hours or a few days.
One of the key things in telling the difference between delirium and dementia is that a person's level of consciousness fluctuates in delirium. They are in and out of consciousness, from awake and alert to sleepy somnolent, to hyperalert and agitated. Sometimes they are difficult to wake up, and may go from sound asleep and difficult to rouse to extremely agitated in a matter of seconds.
A person with dementia typically will not go in and out of consciousness so abruptly. They will be awake and alert, maybe completely impaired with memory, concentration, orientation, but they will be alert.
Another key thing is since delirium is a medical or organic problem, a person with have "autonomic fluctuations"  This means there vital signs will fluctuate a lot over the course of the day. Remember it is a medical problem. So their blood pressure may go up and down they may have fevers that come and go, pulse rate may fluctuate. In someone with dementia only, you would not see much fluctuation in vital signs on a daily basis. But if they are not checked you would not know.
It is something a doctor (or medical provider) really needs to diagnose and find the cause of and treat.
As I have stated ion previous blog posts auditory hallucinations are typically associated with a psychiatric disorder, that is "hearing voices" of people that are not there. Unfortunately visual versus auditory hallucinations are not always distinguished by medical people outside of the psychiatric realm of specialists. Hence you can see another reason why it gets confusing.
Delusions are a symptom of psychosis. They are false ideas or beliefs. They can be of different types. Paranoid- eg "aliens planted a computer in my brain" or Ssomatic (physical) there are snakes in my belly eating my insides" Delusions are typically asassociated with a psychiatric disorder, such as schizophrenia, they are fixed and ongoing, however they can also develop in someone with dementia. And in fact are not uncommon as Alzheimer's disease progresses.
Delusions can also be seen in a delirium, but there are so many other things going on when a person has a delirium a fixed delusional belief is usually not a paramount symptom, since the whole medical problem is quickly developing and acute.
The paranoia associtated with for example Alzheimer's is a little bit different say than someone with schizophrenia. The false beliefs in dementia, may be more variable, and less fixed and tend to come and go, more than in a functional psychiatric disease.
but the issue of delusional beliefs is one of those quandaries that makes everyone ask is Alzheimer's a medical or a psychiatric problem (see previous posts).
The delusional material is often treated with anti-psychotics, it may not completely go away, but the person tends to be much less obsessed concerned with or likely to act on their delusional beliefs if they are treated. We then run into all the problems and well publicized issues with antipsychoitcs and the warnings in the elderly etc. (see previous posts).
Hallucinations are also treated with antipsychotics, they are not quite so common in dementia but certainly can and do occur, maybe not as often as delusional beliefs though.
you would not want to start treating visual hallucinations without simultaneously find the cause of any delirium. Auditory again are more common in psychiatric disorders, and it is less likely to find a delirium or medical cause, so the hallucinations are treated there also, and often respond quite well to antipsychoitc meds.
Depression is a psychiatric disorder, that is now more openly talked about over the last 15 years or so, so it has made its way into the mainstream of primary care and is regularly more screened for in general medicine, It is much more socially acceptable to talk about depression. Depression can have a high morbidity- loss of job, divorce, substance abuse) and be fatal for example by suicide if it is not treated. 
Persons with dementia can also develop depression, but often unlike someone without dementia they can't necessarily tell us about it or how bad they fell because they are already cognitively impaired.
Here is where it gets even more tricky. Back in the day not so long ago, there used to be a common term called "pseudo-dementia". It was associated with depression. In fact it still is, but the term is no vogue anymore. Probably too confusing for everyone. Here's what it means- a person with depression has lots of symptoms- sad, hopeless, helpless, suicidal, insomnia, low energy, weight loss, for example to name a few, but a person suffering from major depression can also be cognitively slowed. They can be sluggish in memory and thinking. It can be mistaken for dementia,
As a person ages they are at increased risk for developing Alzheimer's, but if they are depressed and have absolutely no dementia, they may still have cognitive slowing from the depression and be misdiagnosed with dementia. IT HAPPENS A LOT. With the health care debacle it will happen even more as we will tend to want to diagnose ourselves or have our friends do it. This is why a medical work-up and psychiatric work up and evaluation is so important.
With health care rationing already here, I am very fearful that there will be many people misdiagnosed or simply not treated. People with Alzheimer's being misdiagnosed with depression and vice versa
Now one final problem, a person can have Alzheimer's disease brewing and depression at the same time. In fact depression can be the first sign of Alzheimer's. The diagnosis of one or both has to be made and differentiated by a medical professional. untreated depression can make the Alzheimer's worse.