So apricot is prlprl on a chestnut(red, ee) base.
Palomino is one creme gene on a redt base, so ee CcrC.
Creme an incomplete dominant, so it'll look different depending on whether a horse has one or two dominant genes. CcrC becomes palomino, buckskin, and smokey black on chestnut, bay, and black base coats, respectively.
CcrCcr becomes cremello, perlino, smokey creme on chestnut, bay, and black base coats, respectively.
Ata and AtAt are brown agouti, which turns bay into brown or seal brown. CcrC on seal brown becomes seal brown buckskin, and CcrCcr becomes brown creme, like your girl.
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Now, pearl is recessive and acts with creme. So Prlprl won't show up on its own, but paired with CcrC you get palomino pearl, buckskin pearl, and smokey black pearl, which look very similar to their PrlPrl CcrCcr counterparts mentioned above.
prlprl acts only on red coats and has no effect on black pigments. Technically, bay is black based but with the agouti modifier, which restricts the black pigment to the legs and ear tips, or black points.
prlprl on a red coat is apricot; if each parent has one prl - Prlprl - there's a 25% chance of getting prlprl, 25% chance of PrlPrl, and 50% chance of Prlprl. Factoring this in with possible E and/or Ccr genes they may have, it's possible to get an apricot from Ee aa Prlprl CcrC x Ee AA Prlprl CC, though the chances are slim.
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And lastly chocolate palomino is just a phenotype thing, like bay and chestnut variants :)
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I hope I've covered enough, but I'd be happy to answer any other questions you have!<3
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