First picture looks like an apple that was cut off a couple feet above the ground, then all the regrowth was left to run wild. Second picture also looks like apple, so I am thinking a flowering crab. Then the fruit in the third picture doesn't look like an apple--do the fruit have a blossom end that isn't showing?

All the pictures look like Malus to me. If you cut a fruit in half through the 'equator' it will have a star like pattern with separate seeds if it is a Malus.

It's definitely something you can graft good fruit to. I'm 95% sure it's an apple rootstock because of the slightly red wood and fruit and the leaf. Something that is close to this and could possibly fool me is the callery pear but I'm 80% sure that's not what it is. Pear leaves are more round and the leaf would likely still be red. The callery frut would still hang and look similar but is not red nor is it's bark. The reason why I'm not 100% sure is because with wild trees they vary greatly. I would graft apple scions on the tree using a rind grafting technique.

Here is a link that might be useful: Rind Graft technique

I'm always amazed at the level of expertise-and the willingness to share it- in this forum, so thank you for trying to help me here. 1.) It was cut and left to run wild. All 3 photos are from the same tree, to be clear. There is no blossom end. I have some Bradford pears and their little fruit have those blossom ends, but they look very different from these fruits except they are about the same size.
2) Unfortunately, I waited so long to ask for help with this that the fruits have rotted inside to the point that I can't tell what the seed situation is/was. Its all kind of mush now.
3) The wood really doesn't look reddish in person, that's more of a photo thing I guess.

BEFORE THIS THREAD DIES...PLEASE help clarify something: The real reason I wanted to identify the kind of fruit tree this is was so that I could graft something to it. However, ClarkinKS made it sound as if I can do that even if I'm not sure what it is.....IS THAT TRUE? If so, please let me know what kind of fruit you think would be easiest for a beginner to graft to this tree. I have several apples so I'd prefer cherry or pear or plum but if apple is more likely to succeed I'd be happy to do apple. Thanks folks!

I think the tree is in apple and that is what I would graft to it. I'm not a 100 percent certain that a wild apple will even take apple scion wood from a tame tree because there is no guarantee they are compatible . By the looks of the tree I'm guessing someone tried it before. I know with 100 percent certainty it won't grow apples if you don't graft it over. Apples and pears are not compatible with each other. They would likely grow a while and eventually the graft will fail. There are trees such as some plums that are partially compatible with peaches etc. apples and pears cannot be grafted to each other.

Post some additional pictures if you would of the fruit opened up, seeds of fruit etc. and we might be able to tell more. Wild crabapple and callery pear fruit both hang on the tree and have similar appearance. You can wait a year and know for sure. Callery pear seeds look slightly different from apple so you can compare them

my bet is apple. graft some of each, and you will find out.

That is definitely an apple tree. I have seen many wild apples with fruits that size. They probably even taste good this time of year when they are soft and mushy.
I've grafted lots of apples onto wild rootstocks like that. It usually works great.