STC is a GENERAL rating of sound isolation - it means different things at different frequencies. It was originally intended to block voice-range frequencies in residential areas, so is centered around 500 hZ - I have yet to see an actual formula for calculating STC. However, normally if the TL (Transmission Loss) of a wall is 52 dB @ 500 hZ, then the STC of that wall will (usually)also be 52 dB.
The difference is that STC is a "one size fits all" number designed to show the isolation for voice frequency ranges, where TL is measured and defined at several different frequencies. TL, in order to be valid, MUST state the frequency it refers to.
For today's music isolation, STC isn't the best measurement - When it was developed, there were no SUBWOOFERS, and hip-hop hadn't been born yet. There have been attempts at getting a NEW standard of wall ratings approved, but little support for the usual (dollar driven, mostly) reasons - this is called MTC, and stands for either Music Transmission Class or Machinery Transmission Class. Both take into account the lower frequencies involved in the classification.
Just because a wall is rated at 55 dB STC, does NOT mean it will reduce sound by 55 dB - this varies with the frequency, and is MUCH lower at low frequencies - That would make things seem like you couldn't stop drum noise very well, but the human hearing response (sorta) steps in and "saves the day" - humans don't hear as well at lower frequencies, nor at lower volume levels at those low frequencies - so a lesser reduction in sound at lower frequencies isn't as bad as you would think.
There are 'way more factors involved in isolation construction (I don't like the term "sound proofing", it infers you can TOTALLY block sound and I doubt ANY of us here could afford to do that) - For drum isolation, the lower frequencies pose a problem of more vibration getting into the building's framing, which can then vibrate walls in other rooms and result in what's called "flanking noise" - the term means the same as in war, where you try to "flank" the enemy (get around his defenses) - This is where the "room in a room" concept comes in. If you can keep the sound from ever GETTING to the framing/foundation of the building, then it CAN'T vibrate wall panels in other rooms. Problem solved.
Sorry for the length, that was probably 'way more than anyone asked for, and 'way less than there is... Steve