Same size, different chemistry
Both are about 6.8 × 2.15 mm — thinner than the LR626 / SR626SW pair. LR621 (also AG1 / LR60) is alkaline (~1.5 V).
SR621SW is silver oxide (~1.55 V), commonly sold as 364. Thin quartz watches that name 364 / SR621SW want silver oxide, not alkaline AG1.
Examples on this site
Casio EF-305 and multiple Seiko calibers (e.g. 6N01 / SUR609 family) on this site use SR621SW — not LR621.
Do not use list
Do not treat 364 / SR621SW as an LR621 / AG1 equivalent without checking the device.
Do not confuse this thin pair with taller LR626 / SR626SW (≈2.6 mm) cells.