Is there a term for the "default" articulation that is played when no articulation symbols are present? When the note is played for nearly its full duration value, but with just a tiny rest to separate it from the next note.
'Normal' playing is somewhat like speaking normally. Notes flow into each other - there doesn't need to be even that tiny rest you mention. Most times, notes can be given their full duration value, and if a writer wanted something different, he would write shorter notes and rests, or put staccato marks. Imagine a trumpet or sax player not joining up notes in a phrase? Sometimes it's necessary, due to limitations of the instrument or large jumps in pitch, but generally, legato is the default way to play.
While Tim is correct that many players simply play legato by default, that is clearly not what you’re describing.
What you’re describing would simply be called non-legato (meaning not short but also not slurred).
What you describe would be the default in 18th century German/Austrian repertoire, at which time it was called “regular touch”. Note that the absence of articulation markings does not mean you have to constantly play regular tough; articulation was left up to the performer to a large extent.
For most nineteenth century London repertoire for example, I would say legato is the default.
In the twentieth century composers tend to be more explicit.
In conclusion, what you describe is not “the” default but would be called non-legato.