That 63 A is the continuous current it carries without tripping; the Curve C means the magnetic trip fires between 5 and 10 times the rated current — typically 315 to 630 A — which catches moderate inrush from motor starters and transformers without nuisance tripping on start-up. That puts it in the high-fault category, suited for industrial panels with large upstream transformers or close-coupled distribution. Two poles means it switches both line conductors — common for single-phase 230 V AC branch circuits or for protecting two legs of a three-phase system where you need independent overcurrent protection per phase.
The S202M-C63 shares the same 63 A and Curve C but is a standard-series breaker with only 6 kA interrupting at 277 V AC — one-eighth the fault-clearing ability of the S802S-C63. The S202P-K32 is a 32 A Curve K breaker (magnetic trip at 8–12x In) with 10 kA interrupting — a different animal entirely, sized for smaller inductive loads and lower fault duty. The S802S-C63 is the right call where you need the full 63 A pass-through and the high interrupting rating.
Two-pole width means it occupies two 17.5 mm module spaces — 35 mm total.