Making bread in a bread maker using regular yeast not bread maker yeast

There is certainly a difference between different yeasts. Different kinds of yeast react differently, are "happy" at different temperature ranges, produce different amounts of gas, live for different amounts of time. In my little world, however, it's better to use a yeast that you use commonly and understand than it is to experiment with a different yeast that may not behave the way you expect.

The thing is "baker's yeast" is a generic term. If it called for rapid rise yeast, and all you had was active dry yeast, I'd say to go out and buy some, or your bread would become flat. Chances are, you have one of those two kinds. They both work in most recipes, but each have their peculiarities, and you need to adjust.

I'd give it a shot, and see how it comes out. If your bread ends up "whacky", then try something else.

You can sort of substitute, yes. Bear in mind that cornbread has a far lower gluten content than wheat breads (zero gluten if there's no wheat flour in the recipe), and thus will not hold together quite as well. So you may wish to use slightly less of the custard base.

In addition, I've found that cornbread doesn't generally make a particularly nice sweet pudding; it's much better in a savoury application. So perhaps throw in some jalapeno and some goat cheese.