First part:
Well yes, but still the simulation may have stepped multiple times in one update(), and the renderer only interpolates between last and current state. So there will be one or more states that do not get displayed. Lets say update() does 3 physics steps, 1,2,3 - then the renderer will after that interpolate between 2 and 3, but what happens from 1 to 2 will not be rendered. Kind of a frameskip.
Example, imagine player moving with speed of 1:
realtime simulationframe renderedframe visual_playerpos shouldbe_playerpos
0 0 0-0 0 0
1 - - - 1
2 1,2 1-2 2 2
3 3 2-3 3 3
4 - - - 4
5 - - - 5
6 4,5,6 5-6 6 6
7 7 6-7 7 7
So this means that even though with this method the player is at the correct position at the right time, sometimes the frames that show how he got there will be skipped.
This will make it look a little jumpy/jittery,especially with fast movement.
You can check this by looking at the time between rendered frames - idealy this would be near constant, but it probably won't be. in the above example 2 frames will stay longer on screen than the others.
Second part:
Simulation time would be the current time of the physics simulation or the current state, rendertime would be the time the renderer actually displays. With the loop as you have it now, rendertime is always <= simtime but >= simtime-timeDelta, and should be almost exactly timeDelta behind realtime. with a fixed timestep like yours simulation time is always a multiple of timeDelta.
So by that definition you have 3 times already, sim, render and real-time. Even if all three just describe points on the same timescale.
realtime would be "now".
simtime would be whatever is left in the accumulator behind realtime.
rendertime would be timeDelta behind realtime.
Hm,yes, a little confusing maybe, i'm not the greatest explainer.
Anyway you got this basically: http://gafferongames.com/game-physics/fix-your-timestep/ (good read btw, and generally the way to go)
Now you could go one step further and decouple some more by having the renderer run at it's own fixed speed to get rid of that last bit of jitter in time between frames.
BTW, have you checked if the jitter is also noticeable when running fullscreen with vsync active?
Also, do you sleep() somewhere if stuff happens too fast/system is too powerfull? Can also help to stabilize framerate.