Is the battery used for FN310 same as that of YTA510 , EJX wireless transmitters and YTMX580?

It is the same battery. TL-5930/S of TADIRAN is used.  The battery case used by the FN310 and FN510 is different from the YTA510, EJX series and YTMX580.

The YCA part number for two batteries only (no case), is F9915NR.

The YCA part number for battery pack with two batteries for YTA510, EJX-B series, and YTMX580, is F9915NQ.

The YCA part number for the YTA510, EJX-B series, and YTMX580 battery case only (no batteries), is F9915NK.

The YCA part number for the FN310 and FN510 battery case only is F9090GD.