Same size, different chemistry
Both are about 11.6 × 3.1 mm. LR1130 alkaline is also sold as AG10 / LR54 / 189 — Casio MS-20YC / SL-310YC use LR54/LR1130 as a solar backup cell.
SR1130 silver oxide is also sold as 389 / 390 / SR54. Legacy calculators that name G-10 / SR1130 / 389 want silver oxide, not AG10 alkaline.
Not LR44 / 357
LR44 / SR44 are the same diameter family but much thicker (~5.4 mm). See LR1130 vs LR44 and LR44 vs SR44 — do not use those pages as an SR1130 answer.
Do not use list
Do not treat AG10 / LR1130 as a 389 / SR1130 equivalent (or the reverse) without checking the device.
Do not flatten “AG10 = 389 = LR1130 = SR1130” retail lists into typed equivalence.