Okay, the difference between TB and RTwP in a nutshell:
TB
- each combatant is allotted a certain number of actions (or APs)
- actions are executed immediately
- combatants act in sequence
RTwP
- number of actions that can be performed depends on time (duration, reactions, etc)
- actions can be queued during the pause
- combatants act simultaneously
It's really not complicated. It basically boils down to two very simple concepts:
TB: combatants act in sequence
RT: combatants act simultaneously
The pause only allows you to queue actions, which becomes necessary when the actions become too complex to command in real time -- and of course it lets you take a step back and analyse the situation.
TB: chess, poker
RT: basketball, rugby
RTwP is like regular RT except you can shout "HOLD!" at any moment and the gameplay freezes so you can consider your options.
RT is about twitch-action, TB is about strategy. RTwP is about twitch-action but with pauses to accommodate players with slower reactions (or just scenarios that would be inhumanly difficult in plain RT).
RTwP is an attempt to remove the weaknesses RT has in comparison to TB without losing the focus on action (because that's what RB is about: adrenaline rushes, shock, suspense, etc -- TB games need to be creative in order to replicate those effects whereas it's pretty much inherent for RT games).