David
Welcome to the Forum. Basically, a Mounted Infantryman is a soldier who rides a horse or pony into action, dismounts and engages the enemy. A cavalryman, in contrast, generally fights from horseback. Mounted Infantry (M.I.) were extensively used during the ABW. I suggest you have a look for Spiers' "The Late Victorian Army 1868 - 1902" for more detail on the MI concept and implementation during 1899-1902.
A glance at the Scots' Guards medal roll for the ABW (WO100/165 page 261) shows your GF Pte. J.B. Braid as being a member of No.1 Coy. Scots' Guards, Guards Mounted Infantry; his section being commanded by Lt. C.W.Coke. As you say, his QSA clasp entitlement was three, CC, SA1901 and SA1902. His regimental number was 3346.
The aforementioned Lt. Coke is noted elsewhere as having active service in Cape Colony between 12/1901 and 5/1902 - so it is reasonable to assume that so long as your GF remained with No.1 Coy., his service would have been similar to that of his officer.
Good luck with your quest to find your GF's medals.
Regards
IL.