Short answer
If the movement or empty cell says 381 / 391 / SR1120SW, buy silver oxide — not alkaline LR55 / AG8 / LR1120.
LR1120 on a blister is usually the alkaline AG8 / LR55 label — not a second silver-oxide code.
Same size, different chemistry
Both are about 11.6 × 2.1 mm — thinner than SR43 / LR43 and much thinner than LR44 / SR44. LR55 (also AG8 / LR1120) is alkaline (~1.5 V).
SR1120SW is silver oxide (~1.55 V), commonly sold as 381 / 391. Thin quartz watches that name 381 / SR1120SW want silver oxide, not alkaline AG8.
Pack labels that cause the mix-up
AG8 / LR1120 usually mean alkaline LR55 — labelling, not a second size.
381 / 391 usually mean silver-oxide SR1120SW. Charts that print “AG8 = 381 = LR1120 = SR1120SW” as one battery are wrong.
Do not use list
Do not treat 381 / SR1120SW as an LR55 / AG8 equivalent without checking the device.
Do not confuse this thin pair with taller SR43 / LR43 (~4.2 mm) or LR44 / SR44 (~5.4 mm) cells in the same diameter family.