What is the same
Roughly the same diameter (~11.6 mm) and alkaline chemistry family (~1.5 V).
What is different
Height: LR1130 ≈ 3.1 mm; LR44 ≈ 5.4 mm. A wrong height cell will not seat correctly.
Pack aliases differ: LR1130 ↔ AG10 / LR54 / 189; LR44 ↔ AG13 / A76 / L1154.
Do not confuse with silver oxide
357 / SR44 is the silver-oxide size twin of LR44 — not an LR1130 equivalent. See LR44 vs SR44.
Do not use list
Do not substitute LR1130 for LR44 (or the reverse) by diameter alone.
Do not treat retail “LR1130 same as 357 / LR44” lists as typed equivalence.