Yes, it is some tense of spit.
The word spat is a singular common noun. The noun spat is an abstract noun as a word for a small argument. The noun spat is a concrete noun as a word for the cloth or leather covering for men's shoes.
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No, "spat" is not an onomatopoeia. An onomatopoeia is a word that phonetically imitates, resembles or suggests the sound that it describes, like "buzz" or "splash". "Spat" does not directly imitate a sound.
spat
spar spat
Spat, disagreement, squabble, quarrel.
A slight disagreement. A tiff. A spat. In debate, your "Argument" is designed to prove one side of the issue under debate.
A quarrel could be a fight, spat, argument, or conflict.
This could be a tiff or a spat.
Dispute, quarrel, altercation, squabble, fracas, row...
A spat is a minor fight or disagreement.
'Spat' is not a mathematical term.