Direct answer
377 and 376 are the same 6.8 × 2.6 mm silver-oxide size. Their difference is the manufacturer/IEC drain designation: 377 maps to SR626SW low drain, while 376 maps to SR626W higher drain.
Both are 6.8 mm in diameter; heights are 2.6 mm and 2.6 mm. Both are 6.8 × 2.6 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.