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.
Guitar is a three-dimensional instrument, where you are almost forced to know things in multiple locations.
Here's something I think is of paramount importance: when you learn a tune on guitar, you should always practice playing chord and melody 

together. That way you really learn to link the two things together. 
It has to become almost automatic. Then when you improvise, you should be able to see (and play) chords at almost any time as you go by.
About note spelling when you play, I think it has to do with different areas of the brain. 
It's the same thing that happens when you speak another language. These are two different processes: one process is knowing and using that 

language directly, without translating it. The other process is translating what you say into your own native language.
That's what simultaneous interprets do. But they never do the two things together; always sequentially.
So when you play, you bypass the names and go to the heart of things. If you really know these things, you won't need anything else. 
If you listened to music for enough time, you would tell most chords by ear, as if I’m listening to a D chord on the radio I know it’s D. 
And if I can hear their quality, find them on the fretboard, and play them, what else do I need?