Really the differences are mainly a Reddit thing. All calicos are piebald torties, which are black and orange or grey and cream cats. The b (tabico, torbico) are for when the black/grey areas have tabby stripes. All orange/cream areas have stripes, visible or not, so cats without the stripes in the black/grey do not have a b in their coat name - however, the sub voted to allow any tricolors with visible stripes (thus the “honorary” flair). The reasoning for the tor[b/t]ico distinction is purely for appearance differentiation of large, unbroken color patches (calico/tabico) vs brindling (tor). Tortie, calico, and tabby on those are what your vet will call your cat.

Black and orange/grey and cream, generally brindled, little to no white, no stripes in black/grey = tortoiseshell (“tortie”)

Black and orange/grey and cream, generally brindled, little to no white, tabby stripes = torbie

Black and orange/grey and cream in large patches, large white areas, no tabby stripes in black/grey = calico

Black and orange/grey and cream in large patches, large white areas, tabby stripes in black/grey = tabico

Black and orange/grey and cream brindling, large white areas, tabby stripes in black/grey = torbico

ETA: If there white is in a tuxedo pattern, there’s a tuxetabico, tuxetortico, or tuxetorbico. There’s some debate on if these cats are tor[t/b]ies or [cal/tab/tort/torb]icos.