No, they were different.

All four terms specifically signify some crucial factors of the visible keywords on a page.

Keyword density refers to the ratio (percentage) of keywords contained within the total number of indexable words within a web page.

Keyword frequency refers to the number of times a keyword or keyword phrase appears within a web page.

Keyword prominence refers to how prominent keywords are within a web page.

Keyword proximity refers to the closeness between two or more keywords.

In general, the closer the keywords are better as per semantic order.