I will try to explain the difference between the words, but you need to have in mind that they can be used in the same way in many situations. Appropriate means something that is suitable for a certain situation. "Not appropriate" is the opposite and it means something that is unsuitable for a certain situation. "Inappropriate", however, often refers to something that has to do with different kinds of harassment. For example, it is appropriate to ask questions related to language here in italki. It is not appropriate to post personal info or to write a dating advertisement. It is inappropriate to write or post explicit content. An appropriate teacher is a teacher who teaches the language you want to learn. A not appropriate teacher is a teacher who doesn't teach that language or who can't teach you at the level you are at. An inappropriate teacher is someone who isn't acting professionally and doesn't respect his duties as a teacher and crosses your boundaries. Proper has two formal meanings and one slang meaning. The first formal meaning is when something is real or authentic. For example, a proper teacher is someone who has passed a generally recognized teaching exam. This teacher may not be appropriate for your level and preferred language, but he is proper nonetheless because he has the papers. An improper teacher is someone who tries to act as a teacher but either doesn't have the papers or personal skills to be one. The second formal meaning is similar to appropriate: Something that fits a situation. It can be used interchangably with appropriate most of the time, but there are exceptions that I can't come to think of in this moment. The slang meaning of "proper" is "good" or "nice" and "properly" is used for "very".

"Proper" might mean adequate, right, fitting, and "appropriate" can be used just as well, if you're talking about manners, politeness, customs; however, in British English, "proper" can be used as a strengthening element to another word: ex. "I gave it a proper trim/brush/thought".

😂proper is short and simple

I would say that there is a distinct difference between the two words. "Appropriate" is a little easier to define. It means that something is correct for the situation. "When playing music authentic to a certain region, it is important to use the "appropriate" musical instruments. "In Japanese, it is appropriate to use 尊敬語 [sonkeigo] when addressing a superior at work." "That solution sounds appropriate for this problem." "Proper" sometimes means the same as "appropriate": "It is important to use the proper tool for the job." "You shouldn't play hockey without the proper equipment." But sometimes, "proper" means "genuine" or "real" [it's not very common to use "proper" this way in North American English conversation]: "He looked properly apologetic." "He's not a proper doctor."