there are also memes (meaning the kind intended to be funny on the internet in this case) which dont use images at all but are just a recurring reference or something like that. it is largely the same idea as the original meaning of the term but on the internet it generally refers to things that are intended to be funny (in recent years, usually through self-reference as a result of algorithm-based social media).

usually a square image with optional text.

Thats an image macro which is a specific type of Internet meme. Although I’ve never heard of someone suggesting they must be square; that seems very odd. Are the meme police checking height:width ratios now?