Direct answer
371/SR920SW and 370/SR920W share 9.5 × 2.05 mm dimensions and silver-oxide chemistry. The SW/W suffix is the only listed classification difference, but it is material to watch-movement selection.
Both are 9.5 mm in diameter; heights are 2.05 mm and 2.05 mm. Both are 9.5 × 2.05 mm silver oxide / zinc cells at 1.55 V nominal, but their drain designations differ (SW: low-drain profile versus W: higher-drain profile). Preserve the device-specified class.
Do not infer acceptability from fit alone. The device maker’s complete code and current instructions remain authoritative.