biggie2207 said:
Will the battery and the motor have the same gauge wire? What gauge will they be?
Without links to the exact ones you bought, we can't be certain (probably not even with the links if they don't provide this info), but it is likely they are something between 18g and 12g.
If they are a step up or down, will that be a problem?
No, if you mean in the matter of installing matching connectors.
Since you're pretty much stuck with the existing wires (unless you open things up to completely replace them all the way to the internal connection points, which risks damage and usually voids warranties), it's simply that the highest gauge number (smallest wire) determines the highest current that can continuously be passed thru it.
As long as it's thick enough for the intended current of the item it's connected to, then that won't be a problem anyway, as that item couldn't handle higher currents anyway.
A random example: if the motor had wire suitable for 20A max continuous, and was only capable of demanding 18A, it wouldn't ever draw more than 18A anyway, so the 20A max wire would be fine. If the battery had wire suitable for 15A max, and the battery was only capable of 10A, then again it wouldn't matter if the downstream wire could handle more, as the battery wouldn't be able to output more than that anyway (not without problems of it's own).
Also bonus points if you know any stores locally that sell connectors since I will only need 2 not a whole pack.
Since the only location you give is "USA" in your profile, with no further info in your post, it's a little tough to give you a "local" recommendation.
But, if you check around your local area for any ham-radio (amateur radio) enthusiasts or clubs, Anderson PP45s are a common connector they may use, and as such they may have spares they'd sell.
If you're looking for other Anderson types (they make quite a few), you'd need to specify the one you're after for specific help with those.
As Mark5 notes, there's a lot of places selling them on the internet, including places like Powerwerx.