The main difference between Evil Spirits and Demons are their origins - to put it simply. Evil spirits have normally been in physical human form*, demons have never been born into the physical planes, but have their source elsewhere - they can however manifest in various ways in the physical realms.
Having said this, I don't totally dismiss the theory that many cases of evil spirits/discarnate humans do have demonic forces working through them - a case of like attracting like. It is similar to the theory that people who have health issues such as addictions, alcoholism etc.. have at the route of their problem some form of 'demonic force'.
As a final thought, I do feel that within humans there is the potential for evil that does not have its origins with demons or anything else. Sadly, this dark area is totally human using 'demons' as an excuse in order that we can escape facing the reality of our own darkness. This darkness within may well be like a beacon that attracts evil spiritual forces.
Hope this helps.
*Evil spirits can also have other forms other than human/demonic but this would sidetrack your question too much.