How do caraway and ajwain differ in taste and use?

You are right about Ajwain and Caraway seeds, they are very different when it comes to taste; although both are considered as good digestives and add a distinct flavor to the dish.

Coming to your two questions @Neil hinted about how they taste. As its hard to describe how exactly they taste, I will mention how I used them.

I have used Ajwain when making concotions or when I am making chilli dumplings (mirchi bajji in regional language) with gram flour as they aid digestion of flour.

Caraway, I usually put a pinch of these when cooking rice as its gives nice aroma to the final dish you make, example tomato rice(rice mixed with some veggies and other Indian spices), meat pilaf's etc.

Although I cannot think of any real substitute to Ajwain, you can try adding some cumin seeds which is somewhat close. Hope this helps, happy cooking.