I would deem the translation misleading, to be honest. There are no definitions, really, this is simply a technical usage of language which is historical. That's why it is hard to pin down any sources discussing this as well, it is simply taken as a given.
On "XXX überhaupt" (XXX in general/as such)
There is one hint available in Ottfried Höffe's German commentary Kants Kritik der reinen Vernunft: Die Grundlegung der modernen Philosophie:
Da es in keinem der vier Raumargumente um einen näher qualifizierten, etwa dreidimensionalen Euklidischen Raum geht, hätte Kant statt von Raum besser von Raum überhaupt oder von Räumlichkeit gesprochen. (Höffe 2004: 87)
Since none of the four arguments about space is further specified as being about, for example, three-dimensional Euclidean space, Kant should have talked about space as such [Raum überhaupt], or spatiality [Räumlichkeit], instead of [simply talking about] space.
This suggests that Kant uses (or should always use, to make himself more clear) the suffix "überhaupt" - which I would, therefore, translate as "as such" (a more nuanced discussion of this choice can be found below) - to distinguish between particular understandings of a term and assertions about the concept itself in its most general meaning.
[Personal note: While Höffe is technically not wrong, any other than (relative) Euclidean space was not conceivable at that time afaik. It is questionable whether "Raum" is as ambiguous as he suggests here]
On "allgemein" (general)
I am sure there are sources for this as well, but I am short of having the time to track them down atm:
Kant studied law, which as a huge impact on his usage of language, e.g. in "deduction". The same applies for "allgemein" [general], which usually means "valid without exception" or "in all (possible) individual cases/instantiations, this holds". Which, in turn, can be a form of abstraction when the concept of something is built from these general truths about particulars.
Since the terms are closely related, I understand that they are translated similarly as in general/general, but I, personally, would prefer "as such" and "general". I know that this clashes with "an sich" - as such - which means "its being as it really is", but at this point, it conveys the meaning best. In general is simply too weak since it can just as well mean "usually", which runs contrary to what the German term actually does convey. Another option would be 'itself', ie. space itself, but this again has connotations of referring to the being rather than the idea/concept.
That being said, the former term (überhaupt) means that we make an assertion about the concept in the most abstract meaning, the very idea and core of the concept itself, whereas the latter (allgemein) means that we make an assertion about particulars or something built up from/derived from particulars. Of course, something that holds for the concept itself also holds for the particular instances and something that holds universally for all particulars will be part of the concept, but still, the scope of the assertion is different, and so is the structure of any justification for it.
In your example, he is speaking about a general (discursive) concept of space (see CoPJ §77, 5:407), i.e. a concept which is an abstraction of a whole derived from universal truths (truths without exception) about particular "relations between things". It would subsume the particular understandings of what is a "relation between things", i.e. be about relations between things as such (überhaupt). Instead, he insists that what he is speaking about is a pure intuition (albeit said concept of space certainly exists as well, it is just not what he is talking about here, so he discards it completely to avoid misunderstandings, which invites obscurity since he does not further explain why he discards it so vigorously although it is closer to our normal understanding of terms).
Generally, the extensive Kant-Lexikon by Markus Willaschek et al. is a good place to go for terminological questions on Kant if you can read German. I am sure I have a copy somewhere, but wasn't able to find it for the moment being.