The main difference is that a Soloist is a neck thru and a Dinky is a bolt on, that goes all the way up to the top of the line USA Select series.
The USA Select soloists are maple neck thru with an alder body, and the dinky is an alder body and maple bolt on.
You can also the MG series soloist which is a fully mahogony neck thru guitar, but that's not the typical soloist.