SL is just a shifter, which may or may not bolt on to the brake lever assembly.
ST is the combined brake/shifter.
They both came in 738/9.
If you have the ST type, just get some EF ST51's or 65's, of the proper speed.
They come in 2 & 4 "finger" versions.
The 4 finger can be used on either V or Canti brakes, while the 2 finger is V brake only.
There will be either a 2 or 4 in the suffix. Not all vendors list the suffix however.

I've had 51's & 65's on the same bike (after the 51's were stolen, along with the bar, pedals....)
The 65's did shift better. (9 speed)

BTW, if you're interested in going to 9 speed, now would be the time.
All else you would need would be the cassette & chain. Maybe your old cassette & chain have enough miles on them that they are toward the end of their life anyway????