"Saber Tiger" instead of "Sabel Tiger" would be a more correct spelling; it's probably due to the Japanese R/L swapping thing. With サーベルタイガー, they must have actually meant exactly that, though.
It may be confusing that "saber" is the American-English spelling for "sabre".
On the other hand, "Thrasher" was surely a deliberate spelling; it refers to thrash metal.
Especially the enemy and boss names as shown in the manuals of both Gradius 2 and Salamander make it abundantly clear that Konami, or at least a part of the development team, were huge fans of heavy metal music back in the day.
Not only that, but there are other clues like the character "Van Landroth Frehley", which ofcourse is a nod to the guitar player of the band Kiss.
To drive home that point, the Kana is スラッシャー (which would more approach the English pronunciation of "Thrasher") and not something like トラッシャー (which would be "Trasher").
About the "sprite swap", I think you're right - the introduction of the game seems to have both jets mixed up when introducing them.
It makes even more sense when we examine Thrasher's design; it would look a lot more like an actual saber tiger than the white ship that's apparently wrongly presented as being the "Sabel Tiger":
Thanks for sharing your find with us; I never realized this, and I'm sure I wasn't the only one.
I see there's even a mistake in your topic title That just shows how easy these kind of errors slip in. But I think JohnHassink is right, 'Sabel Tiger' does not make any sense and indeed the sprites look swapped. Me myself also never realized it, so indeed not the only one