You don't indicate where you are (what USDA hardiness zone you are in as well). The first plant with the small fruit is either a calamondin or a kumquat. The larger is likely a mandarin (the probabilities vary on what kind, if you're borderline hardiness zone, then a satsuma, but if you're in 10 or good 9, then could be any less cold hardy varieties). Taste, skin (thickness, peeling ability), ripening timeframe could help narrow the mandarin variety. Satsumas (as well as a few other mandarins) are ripe when fully grown and still green. You could choose to test a greenish one and that would help eliminate varieties.

Your trees look healthy. A regular watering schedule if you're in the desert clime of CA, TX, or the southwest may be really important. Regular fert schedule, timed through pre-bloom, bloom, fruit set, and fruit growth with fertilizer with micronutrients.

If your mandarin fruit segments are is dry, you'll need to definitely manage water. But since you're plants look healthy, I'd say, nature is working out pretty good.

The bigger tree is most likely a mandarin of some sort. Due to the small crop on the tree it is probably one of the alternate bearing varieties. Meaning one year, called the on year, the tree will produce a large corp., followed by the off year (rest year) with a small crop.

The small tree looks to be a satsuma tree, which is a type of a mandarin. The fruit on the small tree, could have seedless fruit, and be easy peeling .

You need to fertilize the trees 3 times per growing season (March through August, equally spaced apart.

I’m on Hacienda Heights, CA Zone 10a I believe. I will get pics of the fruits cut open as well.