word usage

The way I read the difference is this -

If you're using a term that has a previously established meaning in the context you're in (such as jargon in a technical field), and you're explaining that meaning to someone, you would say "In this context, [term] is referring to [meaning]." and similar constructions.

If you want to use a term and give it a new meaning different than its usual meaning, you define it for your audience by saying "For this context, [term] means [definition]." and similar contexts.

Both are commonly used by mathematicians, where we use notation and terms differently depending on what type of objects we're dealing with. The first example would be where we're using a commonly used definition, and the latter would be where we're defining something for our audience for our talk or paper at hand.