Same size, different chemistry
Both are about 11.6 × 5.4 mm button cells. LR44 is alkaline (~1.5 V). SR44 is silver oxide (~1.55 V) and is often sold as 357 or 303.
A device that names SR44 / 357 may run poorly or briefly on alkaline LR44 even when the cell fits. Prefer the chemistry the maker specifies.
Do not use list
Do not treat 357 / SR44 as an LR44 equivalent (or the reverse) without checking the device.
Do not confuse either cell with thinner LR1130 / AG10 cells — same diameter family, different height.