Same size, different chemistry
Both are about 6.8 × 2.6 mm button cells. LR626 (also AG4 / LR66) is alkaline (~1.5 V) with a sloping discharge curve — common in low-cost gadgets and toys.
SR626SW is silver oxide (~1.55 V), often printed 377 / 377A on retail packs. Watches and precision tools that name 377 / SR626SW expect the flatter silver-oxide curve.
Examples on this site
Casio MQ-24 and several Seiko / Orient calibers on this site name SR626SW / 377-class silver oxide — not LR626 alkaline.
If a manual says only “AG4” without chemistry, check whether the maker meant alkaline AG4 or used AG4 loosely for the silver-oxide size twin.
Do not use list
Do not treat 377 / SR626SW as an LR626 / AG4 equivalent (or the reverse) without checking the device.
Do not flatten retail “AG4 = 377 = LR626 = SR626SW” charts into typed equivalence.