The following descriptions from my profiles of the species should help.
Barbonymus altus
This species is probably the one usually encountered in the hobby as the "Tinfoil Barb." The other species is Barbonymus schwanenfeldii, and the two are very similar. The subject species (B. altus) body colouration is more golden, and the red caudal fin does not have the distinct black submarginal stripe along both lobes as on B. schwanenfeldii, whose body colouration is more silvery than golden. The subject fish is also half the size of the other at maturity.
Barbonymus is a contraction [Barb] of the earlier Barbus, plus anonymous [Latin, from the Greek anonumos] meaning anonym ("without name").
In 1937, H.W. Fowler described this fish as another species, Barbus foxi, but this was determined to be the same species as B. altus by Rainboth in 1996. B. foxi continued to be afforded distinct species status in a few sources, until Maurice Kottelat (2001) returned it to the status of synonym for B. altus.
Barbonymus schwanenfeldii
This species is very similar to Barbonymus altus. The subject species' body colouration is more silvery, and the red caudal fin has a distinct black submarginal stripe along both lobes; this is absent on B. altus, whose colouration is more golden than silver. As noted below, the common name of Tinfoil Barb is often applied to other species including B. altus.
This species was originally described in 1853 by P. Bleeker who placed it in the genus Barbus; the species epithet was later spelled schwanefeldii by Bleeker and others, but corrected to schwanenfeldii by T.R. Roberts in 1989 when he moved it into the genus Puntius. In 1993, Maurice Kottelat et.al. assigned the species to the Barbodes genus, but this too did not last long. In his 1999 paper on the nomenclature of the genera Barbodes, Cyclocheilichthys, Rasbora and Chonerhinos, Kottelat erected the new genus Barbonymus; B. schwanenfeldii was the type species for the new genus, and in it Kottelat also placed three other species, B. altus, B. collingwoodii and B. gonionotus; these species had also originally been assigned to Barbus. It is not uncommon to see any of these species offered as the "Tinfoil Barb," though the latter two are very rare in the hobby. Dr. Kottelat determined that these four species form a distinct evolutionary lineage different from the other barbs, actually close to the common carp; but it is not certain whether or not this lineage is monophyletic. Monophyletic means a taxon (here, species) that forms a clade, meaning that it contains an ancestor and all of its descendants.
In 1902, L.L. Vaillant described a variant as Barbus schwanefeldii rubra, but Roberts (1989) determined this was the same species and this name now has the status of a synonym of Barbonymus schwanenfeldii (Bleeker 1853).