"For the full context, see this."
For the complete context, see this."
Are both identical in meaning?
Do I need the article "the"?
Though they are nearly identical in meaning, this NGram shows that "full context" is overwhelmingly preferred. And yes, you do need the article "the" if you don't want to sound clipped.
Both are absolutely correct. I prefer the second one, but I'm not sure why. Both sentences sound wrong without the. Sometimes we do use the noun context without the definite article, but since here it refers to a specific thing, namely the thing which the word this points to, it's appropriate.