Question: When playing guitar,especially improvising,is it best to think of the notes a actual lettered notes or Scale degrees related to a tonic ? Since the keys are easily movable , I'm thinking that its better just to know the degree you want to play and knowing where that is related to the tonic.

Answer: 
With the guitar being a positional instrument, meaning one can play the same tune in many different keys but retain the same fingering and strings, merely moving where on the neck the tune is played, then knowing note names as the tune unfolds is not necessary. The relationship between the tonic and other notes, as far as where they are relatively speaking, fret and string, is easier to remember. In fact, there is often no need to reference from the tonic, but from the last note played. A lot of the time the next note will either be on the same string or an adjacent one, so knowing the various scale patterns is far more useful for improv. than the names of the notes. That's the academic side which (in my opinion) doesn't often come into play (sorry for the pun) during improvising.
It probably depends on how you 'hear' music.

For example ...

Absolute pitch :

I have recently been playing with a folk vocalist who doen'st play an instrument so we spent a bit of time getting the song into the right key for her. Her first choice was always pretty much the orignal key of a recording she'd learnt from - any other key felt 'odd', implying she might have something like perfect pitch. I think at that stage at least she's hearing music kind of in absolute terms : eg a C is a C , not a D even if you transpose. If your'e like this then perhaps it's more comfortable to work out the individual notes and get to know the fretboard that way. That's a lot to remeber though.

Relative to Tonic :

If you're able to hear the interval between the tonic and the notes of a tune (eg it's a 3rd. . then a 5th then a bent-up 7th rrelative to the tonic .. ) then maybe this is the way to think of your scales.

Relative to the last note :

Up two tones, down a full tone . .etc
This seems a bit alien to me in that there's little notion of a "Home" note (ie the tonic) but if that's how you hear tunes then maybe this is a way forward.

To me, thinking in terms of an interval from the tonic is most intuitive as it means remembering only one instance of a scale, and is transferrable up and down the neck. The relevant scale becomes a "shape" of notes on the neck whcih makes life easier.

It also works on other instruments, although if you move to a piano you start to see that pianists may think in terms of absolutes, or have to remeber different 'shapes' for each key as the black/white notes translate to different patterns depending on the key.