Recital is a type of music concerts, usually referring to a solo performance by a musician (sometimes accompanied by other instrumentalists) where the repertoires would be more personalized, and typically lasts for about an hour.
Unaccompanied Solo refers to a piece that is played without accompaniment while the piece is typically composed for a "melodic instrument", such as violin.
The term "Unaccompanied Solo" are usually used in Western classical music, such as Bach's "6 Sonatas and Partitas for Solo Violin" and Ysaÿe's "6 Sonatas for Solo Violin". These works require the performer to have advanced musical knowledge and performance skills, as they need to be able to interpret the piece without the support of other instruments, sometimes even have to deal with the harmony and melody simultaneously.