Is there a difference between fingerstyle and fingerpicking. Due to age I am unable to sing, so which would be more appropiate for solo playing ?
There's not really a difference in the way you mean it. One could maybe say that "fingerstyle" refers to not using a plectrum, but "fingerpicking" doesn't preclude using both. But no matter what word you use, there are different styles and techniques.
For instance a popular beginner technique is to finger some chords in the fretting hand just like you're strumming them but in the picking hand you pick a pattern (thumb, middle, index, ring, etc) and restart the pattern when you change chords.
But a classical or flamenco player would get quite a bit more advanced and precise with it. A jazz player may walk a bass line with the thumb while playing chords and/or melody with the other fingers. A funk or pop player may slap or pop strings like bass player. You get the idea...
Some may use finger/thumb picks or long nails while others only use the pads of their fingers with very short nails. Some use a regular plectrum between their index and thumb and use the other 3 fingers to fingerpick. I do that but also I sometimes use my index and thumb without a pick going back and forth as if I was "alternate picking" with a plectrum.
As far as what to get started with for playing solo … I'd start with the "popular beginner technique" that I mentioned. If and when you want to take it further, that will give you a decent foundation in both your picking technique and achieving some independence between fingers.
Long term I'd look into gradually adding other parts (bass, melody) into the mix. For instance if you have no bass player, maybe you want to add in a bass line or at least alternating the root and 5th. If you are playing a song with a melody and nobody else is singing or playing, then find a way to work it in. Obviously you can't play every part by yourself so compromises need to be made by simplifying the parts. Look into "chord melody" guitar. It's a term that gets used most frequently with jazz guitar but the concept can be applied to other styles as well.
No, they refer to two different but related styles.
Fingerstyle encompasses both the techniques of playing with fingers alone and playing with fingers and a thumb pick. Fingerpicking refers specifically to the style of using only your fingers and does not include the related techniques with the thumb pick.
It is an all-thumbs-are-fingers-but-not-all-fingers-are-thumbs-situation.
Very similar. Some people use those two words as synonyms. Others use them to refer to specific techniques in specific styles. Any style is fine for solo playing. From a beginner's point of view, the more appropriate style is to follow what is taught in your learning-the-guitar material. One of the best beginner's guide (Justin Guitar) will get you started on strumming first, and later add fingerstyle techniques.
Fingerstyle or fingerpicking has nothing to do with whether you put a pick on the tip of your thumb or fingers. Finger"picking" is more inclined to be just a pattern played with the fingers (bare or not), like playing the acoustic part of Dust in the Wind or something. "Travis" picking. Finger"style" however, has become more associated with simultaneously recreated a song for solo guitar, playing bass, rhythm, melody, maybe fills, even solos and percussive elements without the need for accompaniment or vocals (ala Sungha Jung). The poster is obviously interested in playing fingerstyle guitar and there many great lessons and examples on the internet.