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On a seperate issue, I was going to suggest that a Pawn in chess variants might be defined as a usually (fairly weak, slow-moving [along a straight line], and) numerically common piece and/or that can promote. Already with Shogi there are many pieces that can promote (besides Shogi pawns), including some pretty weak ones (such as a Shogi knight). To be honest, I'm not sure how to define a class of 'pawns' in chess variants, except that everyone seems to know a pawn when they see one. :) Perhaps having at least one of the above-mentioned qualities usually suffices, but then again some game(s) may include only one or two units of an otherwise atypical type of 'pawn' in its setup, possibly borrowed from other game(s) that use it more. I haven't seen many games yet where a pawn starts on the first 'rank' of an army; one not-so-obvious function of pawns in the setup of many games is to help initially obstruct the more mobile/powerful units of each army from immediately capturing or harassing one another in some way.

Nonetheless, numerical commonness and/or promoting ability would perhaps be most indicative of being pawn-like; I'd note that in some variants, pawns may have the option of remaining pawns without promoting even upon reaching a promotion rank, and even if they no longer can legally move - this idea was once debated for inclusion in orthodox chess, as in certain rare cases a stalemate might result the next move if a pawn didn't have to promote upon reaching the 8th rank(!).

https://en.wikipedia.org/wiki/Promotion_(chess)#History_of_the_rule

In the following game (Cavalier Chess), non-leaping Ns (commonly known as Chinese Chess Ns, or Maos) are used instead of multiple pawns in the setup, and by the game's rules specially given the ability to promote (compulsory) upon reaching the last rank, and the new piece selected depends on which file on the 8th rank the promoting piece reached - perhaps a border-line case of pieces that at least some might consider to be pawns:

https://www.chessvariants.com/dpieces.dir/cavalier/index.html

Some types of 'pawns' don't have the ability to promote, even, and can possibly make long-distance moves, too. In the following game (Ultima), the 'pawns' are also known as 'pincer pawns' - at least in this game they are the most numerous type of piece in the setup, and move along a straight line (some other game[s], such as Latrunculi XXI, refer to the piece type by another name - it's as a soldier in that game, which starts all of them on the first rank of the setup incidentally[!] - although there are some special rules that make soldiers' capturing abilities at times somewhat greater than in the case of the simpler rules used for Ultima pawns):

https://www.chessvariants.com/other.dir/ultima.html

https://www.chessvariants.com/rules/latrunculi-petteia-xxi