Lipo battery protection/discharge protection

I am fitting a 2S lipo battery into an old RC car that originally had a NiMh battery, and thus, will need to add protection for discharging.

I have these batteries on the way:

https://www.amazon.com/gp/product/B0DGQ638CX/ref=ewc_pr_img_1?smid=A646DVGSXYMNH&psc=1

I am looking at boards like this to wire in my car (pretty typical stuff):

https://www.ebay.com/itm/206038728643

My question: Are the red/black leads in the JST connector "the same as" the red/black leads in the JST/XH connector? I'd like to discharge through the heavier gauge JST connector, which would require me to reference the mid from the XH connector. WIll this work, or do I need to just scrap using the JST connector and discharge through the XH connector?