It's creosote bush but coyote brush

Why

The way I see it, brush is used for a whole mess of bushes. I don't know either of those plants, but maybe the creosote bush can be found growing by itself, whereas the coyote brush will only be found in bunches. There are some types of bushes that only grow in clumps so that may be it.

Just an extrapolation from what I know, mind you, maybe somebody will come up with a better explanation.

bel: Thank you for that, but in my experience neither one is more nor less clumpy than the other

I always believed 'brush' was used for only those bushes that had a particular visual attribute (that is, look like a brush).
In other words, an brush is a bush but not every bush is brush.

And it might well be that it was called that because coyotes have a brush while creosotes do not.

A brush on an animal is a bushy tail, such as that on a fox.

Here's a reply from an acquaintance Russ which in my dotage I don't understand. Can anyone explain why I'm off the track altogether or has he misinterpreted the q:

Okay, I'll put it another way. A single leaf from each of 4 desert shrubberies is placed in front of me and I am asked to say the name of each.
I would say, "A mesquite leaf, a Mormon tea leaf, a coyote brush leaf, and a creosote leaf." I would not say that a single leaf from a creosote bush was a bush, nor that a single leaf from a mesquite tree was a tree, but I still have to say brush to identify a coyote brush leaf.

If I then made a tea from each type of leaf, I would have mesquite tea, Mormon tea tea (stop giggling!), coyote brush tea, and creosote tea.

If I had a big clump sage plants (genus Salvia), it could be a sage brush (A), but that wouldn't turn it into sagebrush (genus Artemisia) (B). Creosote bush is an example of formation (A), coyote brush is an example of (B).

bush vs. brush