They are basically the same. Neither of them are used very often as verbs. In my experience they are usually used when talking about children and their clothes, playing in the mud, for example and sometimes not getting to the bathroom in time. When a football player says "I soiled (or dirtied) my pants" it means they got grass stains on them. If a nurse says "the old man soiled himself in bed" we are not talking about grass stains. I hope that answers your question.

soil - cultivated land dirt - dry soil