Hi Josh,
Excellent question, I'm going to take a stab at clarifying:
+ vs -: these simply refer to whether something is being added (positive) or removed (negative) in an attempt to change the behaviour/induce learning. If you are INTRODUCING spanking, yes, it would be positive since it is the addition.
reinforcement vs punishment: these terms refer to whether you are INCREASING the LIKELIHOOD of the behaviour (reinforcement) or DECREASING the likelihood of the behaviour (punishment).
Therefore, adding spanking would be a positive punishment - i.e. the addition of something (spanking) that has the effect of decreasing the likelihood of the behaviour (at least we hope!).
I recommend drawing out a 2 by 2 table, along the column headers write punishment vs reinforcement, on the row headers write positive vs negative. Then fill in the 4 boxes with the definitions and examples.
See if this helps in relation to Q20. Let me know if you have follow up questions.