Well, of course , around here the locals don't call them AMERICAN WILD PLUM Prunus americana. They are just called plum or wild plum. But the small tree is as Podunk described, hard wood with thorns.
Barton, what you are describing as wild plums is what we call Mexican plum in Texas. It grows in thickets alongside highways, railroads, fencelines, and 1/4 acre thickets in the middle of fields. The growth along fences and highways is probably due to birds dropping the seeds. The bark on the wild plums is slick, but the trunk of the tree may be split an rough as the tree becomes well matured. These wild plums are rarely much more than 8' tall with the tallest being around 10'.
We also have another plum tree that gets 15 to 20 feet tall. It is much more solitary and does not grow in thickets. The bark on the trunks of these trees is very rough, and the fruit appears long after the blooms drop. The plums do not mature until late August or September. They become purple in color, are the size of a marble, and are actually quite tasty. A large tree will produce only a handful of fruit despite being covered in blooms in the spring. That tree that Sunspot posted looks very much like this plum. It will be interesting to see what the bark on the trunk looks like. Now, the kicker is that I have always called this tree a "hog plum," but on doing a search on the internet, I discovered that I've misnamed the tree. Hog plum is what my father called them and I just assumed that was right. Now, I see I was wrong.
Both those trees are in bloom here right now, so I can get pictures for comparison. I'll try to do that today. One thing I know for sure. If you cut down one of these trees with a chainsaw, the wood really stinks.
EDIT: I found some pictures of my "mystery" plum trees from a prior year. Notice how big each tree is and how solitary they grow.
2nd EDIT: DOH! Some days it doesn't pay to get out of bed.

After further investigation, my solitary tree is a Mexican plum or sometimes called a "big tree" plum. The thickets of plums are just called wild plums as you previously noted.

Here is a link to a picture of the Mexican plum's bark. This is quite different from the wild plum's slicker bark.
Mexican Plum
Okay, I'm going away and sulk after making a complete fool of myself.
