The difference between Just and Proper

When used as adverbs, just means only, simply, merely, whereas proper means properly.

When used as adjectives, just means factually right, correct, whereas proper means suited or acceptable to the purpose or circumstances.

Just is also interjection with the meaning: expressing dismay or discontent.

Just is also noun with the meaning: a joust, tournament.

Just is also verb with the meaning: to joust, fight a tournament.

check bellow for the other definitions of Just and Proper

Just as an adjective:

Factually right, correct; factual.

Examples:

"It is a just assessment of the facts."
Just as an adjective:

Rationally right, correct.
Just as an adjective:

Morally right; upright, righteous, equitable; fair.

Examples:

"It looks like a just solution at first glance."
Just as an adjective:

Proper, adequate.

Just as an adverb:

Only, simply, merely.

Examples:

"Plant just a few tomatoes, unless you can freeze or dry them."

"He calls it vermilion, but it's just red to me."
Just as an adverb (sentence adverb):

; simply.

Examples:

"'Just follow the directions on the box."
Just as an adverb (speech act):

Examples:

"I just called to say "hi"."
Just as an adverb (speech act):

.

Examples:

"Lord, we just want to thank You and praise Your Name."
Just as an adverb (degree):

absolutely, positively

Examples:

"It is just splendid!"
Just as an adverb:

Moments ago, recently.

Examples:

"They just left, but you may leave a message at the desk."
Just as an adverb:

By a narrow margin; closely; nearly.

Examples:

"The fastball just missed my head!"

"The piece just might fit."
Just as an adverb:

Exactly, precisely, perfectly.

Examples:

"He wants everything just right for the big day."

Just as a verb:

To joust, fight a tournament.

Examples:

"rfquotek Fairfax"

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