I was listening to this beautiful rendition of "A Man's a Man for a' That" by a singer with a guitar, and it occurred to me that it seemed anachronistic. I tend to think of the guitar as a Spanish (and later American) instrument, that only became popular elsewhere after World War II. So what would a contemporary of Burns have played along with one of his songs?
Probably on a "guittar," also called "English guitar." I've seen it called cittern and cetra, but those are also names for older (similar) instruments.
There's one in "Mrs. Robert Gwillym playing an English guitar," by Joseph Wright of Derby (1766).
I think you can see and hear one in action in this video.
Here's another recording of an instrument at least similar (with a more lively usage).
Take this with a grain of salt. I am not that much into organology (the study of musical instruments) and am completely ignorant of Scottish music. What I know about the 18th century has nothing to do with this kind of music.
There have been plenty of instruments similar to the guitar, and the lineage of the modern guitar can be traced quite some time before WWII, and it was used in more places than in Spain and its colonies in the New World.