Many people seem to confuse the two. I will try to explain in this article what the difference is.
There are many different versions of demons. According to the Christian Bible, a demon is a lesser servant of Satan (sometimes including Satan himself).
In general, demons can be thought of as malevolent spirits, who feeds on or lives of misery and misfortune. They strife to make people suffer, physically, emotionally and/or mentally, by inflicting misfortune and deliberately harming those near them. Some are, of course, more sadistic and harmful than others.
This makes it very dangerous to work with demons. When working with a demon you will typically call upon its help, asking it to harm someone else. The idea is that this is a win/win situation. You get what you want, and the demon thrives by hurting the person you asked it to hurt or attack.
It is very impolite to force a spirit (demon or otherwise) to do anything. When dealing with demons, it is not only very difficult, it is also incredibly stupid. Demons are cunning, vengeful and will probably not tolerate being told what to do. If you succeed in making it obey, you cannot be certain that it is actually bound by your magic. It may be faking it, so that it can get close to you and hurt you even more than it could the other person.
Because demons are cunning, you cannot trust them. They may tell you one thing, but there is no guarantee that it is the truth. Therefore, you should always device a question or another way to determine that the demon is actually who it says it is. If you call upon a demon with a specific name, you may get an answer. But there is no way of knowing that it is actually that demon, and not just a malevolent spirit set out to harm you, who answer; unless you find a way to identify the demon. This could be done by asking it a question about its past. Something it was not prepared for. It will have to identify itself then. There are many other ways to make a spirit identify itself, and you can find a few in the books I list as sources.
On a last note on demons, there is an old saying that should always be heeded when dealing with any type of evocation, but especially demons: Never call up, what you cannot put down.
Never evoke anything, unless you are certain you can effectively get rid of it again.
Some think that daemon is just an exotic way of spelling demon. It is not.
A daemon is a kind of spirit the Greeks believed in. Whenever a person is born, a daemon to that person is created. It is a spiritual guard of sorts, but it has to be called upon and activated. There are a few ways and rituals to call your daemon, but I will not get into them here.
A daemon does not a have specific appearance. It can take any form it wants to, but it cannot manifest physically. It is an etheric being, drifting around you on the astral plane, protecting you from harm. It is not possible for a negative force (in any form) to kill or destroy a daemon. The daemon dies when the person it is protecting dies. However, they are not invincible. They can be incapacitated and harmed by magic or other spirits.
It is possible to call you daemon to your circle, and have it protect you, if you work with something risky or dangerous. This is done as a part of the initial banishing, and is simply an invitation to your daemon to join you. It is best done after the banishing, when the circle is cleansed.
This may seem like a bit of fluff, but I assure you it is not.
The information I have given here can be found in Konstantinos books Nocturnicon and Summoning Spirits: The art of Magickal Evocation.
Thoughts, comments and questions are welcome.
Konstantinos: Summoning Spirits , 2007
Konstantinos: Nocturnicon , 2007
Druehyld, Dannie: Heksens Hndbog (English: The Witchs Handbook) , 1987