Direct answer
303/SR44SW and 357/SR44W share the same 11.6 × 5.4 mm silver-oxide envelope. The manufacturer table preserves 303 as SW low drain and 357 as W higher drain, so they remain separate canonical records.
Both are 11.6 mm in diameter; heights are 5.4 mm and 5.4 mm. Both are 11.6 × 5.4 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.