Fingerstyle guitar?

A "guitar solo" is a, somtimes improvised, passage of music where the guitar is the featured instrument for a few bars - maybe taking over from the singer, or in some forms of music (like jazz) where instrumentalists take turns to play a solo.

Solo guitar means guitar played by itself with no accompanying instruments.

Fingerstyle guitar means playing guitar with the fingers rather than with a pick.

You're talking apples and cars; two different things entirely. Fingerstyle is one type of guitar playing, in contrast to using a pick. Both ways allow for both rhythm playing and soloing.

A solo is not a "style" of playing. Solo by definition means playing alone. Many folks confuse this term with playing "lead". If you are playing with a band you are not playing solo. However something like Eddie Van Halen's Eruption would be a solo, as he is playing that alone. Make sense?

So when a style of playing, you have finger picking, flat picking (using a pick) and hybrid picking (using both a pick and fingers together). So none of these have any comparison to playing lead or solo. Two totally different things. You could play lead or play a solo using any of those 3 techniques.