Meaning of , and ; in relation to defining context
You'd have to check whatever you're reading, but the way I've most commonly seen it used is to separate different contexts.  The rules will then behave differently if a variable or formula is in one context versus another.  mobileink mentioned substructural logics which are often formulated with a context for linear variables and a different context for non-linear variables.

However, ; could simply be being used to separate other things so you don't confuse it with context extension.  Or it could just be part of a term.  Or it could be some operator on contexts distinct from context extension.  Or it could just be this author decided to use ; instead of , for context extension.  Again, what it means is whatever it is defined to mean, which may be nothing on its own.  For example, used to separate different contexts, it's just part of the syntax of a judgement, e.g. the judgement may be 3-ary relation $(-);(-)\vdash (-)$ in which case it makes no more sense to ask what ; means than it would to ask what $.$ means in $\forall x.P(x)$.  See my answer to a similar question for more elaboration on this.