With regard to the somewhat semantic debate as to whether "stab runaway" applied or not, it might be good to not just look at the title of the procedure, but also at any additional information or training which helps define the condition.
For example, on a DIFFERENT aircraft the corresponding AFM procedure starts:
Stabilizer Trim Runaway
Indication:
- Abnormal / uncommanded change in pitch attitude.
- Stabilizer trim changes without pilot input.
- Stabilizer trim changes not by system design (Mach trim, flap compensation, etc).
- Higher or lower than normal and increasing or decreasing pitch control forces.
Thus, while the name of the procedure appears to be narrowly defined, the indications - the conditions under which you are expected to action, or at least consider actioning, the procedure - cover a range of scenarios - and I'll note include the "not by system design" case, so for the B737 STS case, if you know the motion is normal per design, you wouldn't do this procedure. If you don't know that, then it's a contender for "stab runaway"
I don't know if the corresponding B737 materials contain sufficiently similar wording for the comparison to be fully valid ...