It very subtle difference, for "things", which is plural. "Thing" is singular, and is not the same as "stuff", which is plural. It many cases it means the exact same thing, and the usage would change just depending on who is saying it. These are the same. I bought some stuff at the store. I bought some things at the store. I have a lot of things to do. I have a lot of stuff to do. Do you have an specific examples? If you post some we can tell you if "stuff" or "things" can be used correctly.

Stuff is generally plural while thing is generally singular.

"Stuff" and "thing" are both pretty neutral. But "thing" is more positive than "stuff." If I admiring the objects in your home (decorations, toys, pictures, fancy dishes, etc.) I might say, "What nice things you have!" but I would not say "What nice stuff you have!" If your house was really crowded, I might say, "You sure have a lot of stuff." If the objects were old and useless, I might say "What is all this junk?" (and you would say 「スチィーブはしつれします！」) If you came to my house, and I had to move my laptop and books and things from the table before we could sit for coffee, I would say, "Here, let me move my stuff." (Think of "stuff" as a word you would use only if, in Japanese, you would say it without using the honorific お～ or　ご～ ).