I believe that you are referring to the adjective forms of only and sole. It may be that only is more commonly used in English. i think that this may be because only has more collocations, that is nouns with which is works. Similar to the adjective only, the adjective sole must precede a noun. It can have two meanings. The first meaning is exactly the same as only. For example, to be the sole survivor of an accident. Only and sole may be interchangeable in this situation. The second meaning of the adjective sole is that the noun is not shared with anyone else. In this case the adjective only can not be used. This second meaning of sole is only used with certain nouns. For example, to have sole responsibility for a project

As adjectives, they are more or less the same. 'Sole' isn't an adverb though. The adverb form of 'sole' is 'solely'. 'Only' can mean several things as an adverb, but when you're saying there's only one thing to do it means the same thing as 'solely' ex. "I only/solely want to know..." In this case, 'solely' sounds much more formal.

you can use both as they mean the same thing, a sole trader is someone who trades alone. however 99% of the time "only" is the one you want to use :-)