What are the standard connectors used on 12V hobby batteries?
Also called the &quot;(Standard or Large) Tamiya Connector&quot; in R/C speak (ref); not sure if other manufacturers make them (guaranteed someone somewhere does), but here are the Molex part numbers (Digi-Key) for the Wire-to-Wire connectors:
Device Side (usually)

Plug - 35143-0201 (WM2308-ND)
Socket - 35728-0201 (WM2311-ND)

Battery Side

Cap - 35141-0201 (WM2309-ND)
Pin - 35727-0201 (WM2310-ND)

Molex does not make this style in Wire-to-Board; so any knockoffs of just Molex product probably won't either.
An easy-to-use replacement with both Wire-to-Wire and Wire-to-Board that I've used are the Molex Mini MATE-N-LOK 2 connectors (like these), depending on the current you may need regular MATE-N-LOK.