Evil spirits in most traditions would equate to animals while demons would take on a larger or more conscious persuit of their lives. The only exception to that at first glance would be the idea of a spirit as being that being of a deceased human or ghost. This is usually very seperate from the spirits most traditions speak of when using the term.
In asian tradition, spirits are more like manifest emotions or tokens of animals. Evil spirits are usually single minded in their attempts to create problems in mans world but are literally subservient to an educated enough person. Easy to confuse or send away.
In african tradition, spirits are the play things of witches or shamans. Simple animals that again cause torment on the living. It's possible that in some respects, the african ghost in time becomes a spirit through some disconnect to normal human interests. This would explain why the souls of the dead can be used and tooled by powerful witches.
In Austrailian tradition, spirits are large and powerful but not with the same awareness as the living or the conscious. Like big roving beings slow to attract and slower to understand.
North and South America tend to view gods and demons on the same level though really, the demon is a more European term that was brought over with early conquest. Still, the early mezoAmerican civilizations often look to some of their gods as being demonic with blood thirst and the desire to ruin the lives of those who worshipped them. There is little physical difference between the early gods and demons though and it mostly came down to motivation. Spirits were again more animal and often took the form of elements of nature without any real consciousness.
Europe is where the demon things really shines. It was through christianity that all pagan gods became demons and this was likely wherein we have arrived at a definition of a demon as being something powerful, conscious, and evil since christianity tried to imply that anything not christian was therefore a demon trying to trick mankind out of salvation. The christian demons took on the same societal structure as man ironically with dukes and lords and princes but was really just a method of categorizing the various pagan gods and dieties into saints or demons depending on how well they could be used.
Evil spirits in christianity are typically invisible lesser demons: imps, devils, etc. Too low in power to rise to the rank of demon, they simply run around following demonic orders or creating the physical manifestation of a demonic power (ie it's not the demon making the cows milk sour, it's imps that at the request of the demon, frighten the cow nightly and sour it's milk)
