The difference between Apt and Proper

When used as adjectives, apt means suitable, whereas proper means suited or acceptable to the purpose or circumstances.

Apt is also noun with the meaning: an apartment.

Proper is also adverb with the meaning: properly.

check bellow for the other definitions of Apt and Proper

Apt as an adjective:

Suitable; appropriate; fit or fitted; suited.

Examples:

"Tonight there’s a full moon, which is apt, since the election night will bring out the lunatics."
Apt as an adjective (of persons or things):

Having a habitual tendency; habitually liable or likely; disposed towards.
Apt as an adjective:

Ready; especially fitted or qualified (to do something); quick to learn; prompt; expert

Examples:

"a pupil apt to learn"

"an apt scholar"

Proper as an adjective:

Suitable. Suited or acceptable to the purpose or circumstances; fit, suitable. Following the established standards of behavior or manners; correct or decorous.

Examples:

"the proper time to plant potatoes"

"a very proper young lady"
Proper as an adjective:

Possessed, related. Used to designate a particular person, place, or thing. Proper nouns are usually written with an initial capital letter. Pertaining exclusively to a specific thing or person; particular. In the strict sense; within the strict definition or core (of a specified place, taxonomic order, idea, etc). Belonging to oneself or itself; own. Portrayed in natural or usual coloration, as opposed to conventional tinctures. Being strictly part of some other (not necessarily explicitly mentioned, but of definitional importance) thing, and not being the thing itself. Eigen-; designating a function or value which is an eigenfunction or eigenvalue.

Examples:

"usex [[proper subset]] — [[proper ideal]]"
Proper as an adjective:

Accurate, strictly applied. Excellent, of high quality; such as the specific person or thing should ideally be. (Now often merged with later senses.) Attractive, elegant. In the very strictest sense of the word. Utter, complete.

Examples:

"Now that was a proper breakfast."

"When I realized I was wearing my shirt inside out, I felt a proper fool."

Proper as an adverb (UK, colloquial):

properly; thoroughly; completely
Proper as an adverb (nonstandard, colloquial):

properly