We have a 7-year-old, 10' tall avocado tree, grown from a grocery store pit haphazardly planted in the ground by my kids, and it is fruiting right now. However, someone pointed out that it was actually a kumquat plant and not an avocado. We didn't plant a kumquat but my kids had been throwing them at each other way back when and I suppose it is possible that one did take root. Since the plants and fruit look similar at this point, how can we tell them apart without pulling the fruit off and cutting it open? We don't want to waste any precious avocados.

That is Loquat (eryobotrya japonica/rosaceae) not a kumkuat (a type of citrus/rutaceae)
it's a name similarity in sound I guess that is interesting
I really loves Loquat, we call it biwa here, as their name in their native land Japan

I think you mean Loquat as Kumquat is a type of citrus. The leaves on your tree do look more like a Loquat than Avocado. Here's the way to tell without cutting open a fruit: Loquats have a 'belly button' but avocados do not. Go look at the bottom of the fruit.

It does look like a loquat, you're right, but I'm not sure how we would have gotten one of those and the inside of a dropped fruit I cut open a few weeks ago looked like a tiny avocado pit and not a seed. The original avocado pit was planted in a specific place in a small garden. We've always assumed it was an avocado because it grew from that spot a couple months after planting.
Very curious as to what we end up with and how it came about.

Loquats can contain 1, 2 or 3 seeds.

And they were kumquats that my kids were throwing around - small orange-like fruits. I've never seen a loquat before it was mentioned here and I googled it.
Unless I have one. Then I guess I have been looking at one for about seven years now.

Its hard to say what happened in your yard or how the seed got there but if that fruit has a 'belly button' its a loquat. Loquats grow easily from seed and bear fruit in about 8 years. Avocados from seed rarely ever fruit. Hopefully, your loquat has a good flavor - fruit from seed is very variable.

It's a loquat! We cut open the one yellow one and it had a seed and tasted like a kiwi/sour-apple combo. Really delicious.
I'm sad about it not being an avocado but I'm super excited about this new fruit.

Thanks everybody!

Happy eating! I would be happy to have either of those tree in my yard.

I agree, definitely a Loquat (Rhaphiolepis bibas) tree. If you didn't plant the tree, it's probably a gift from the birds! We have a rogue Loquat tree sprouting up in our side yard here in Sebastian and yet I haven't seen trees growing on any neighboring properties around, so a bird probably dropped the seed. I'm not sure we will ever get fruit because it's growing in a heavily shaded area. At our old home where we lived for 36 years, our backyard neighbor had huge Loquat trees all along the fence line and we always had tons of little trees popping up everywhere on our side of the fence. Squirrels love the fruit as well as Gray Catbirds. Years ago, a lady in the office where I worked would make Loquat Jam and bring it to us; it was really good! I can only imagine how many of those small fruits she had to harvest to make jam!

Without a doubt, that is a Loquat tree..