What are the differences between albeit, although, howbeit, however, and though?
These are members of a semantic class called adversatives, which function to flag or acknowledge a kind of dialectical tension or antithesis between two clauses, sentences, or even paragraphs, such that one is or seems to be on one side of an issue or debate, the other on the other side. Among them, but is a coordinating conjunction. Most of the rest are either subordinating conjunctions (e.g., although) or conjunctive adverbs (e.g., however). Mistaking the former for the latter is a common source of error in that it leads to sentence fragments, subordinate clauses punctuated as if they were whole sentences. Though can be either one, depending how it is handled and punctuated:
Though I recruited him, I do not like him. (Correctly used as subordinating conjunction: clause containing it is duly subordinate to main clause within the same sentence.)
I recruited him. I do not like him, though. (Correctly used as conjunctive adverb.)
I recruited him. *Though I do not like him. (2nd punctuated sentence is a fragment, a subordinate clause with no main clause within the same sentence for it to be subordinate to.)
In sum, semantic differences among them are negligible, but grammatical differences keep them from being altogether interchangeable.
Despite is an adversative preposition.
The somewhat archaic albeit is exceptional in being a compound that effectively supplies its own grammatical subject it and subjunctive verb be, as well as the subordinating conjunction al[though], so that only a complement need be supplied to complete a subordinate clause.
The difference is not in the terms but w/their usage. Depending on your audience, the reader will find it interesting that the writer knows how to use both frequently used terms and rare terms properly.
There's a certain language we all use when talking to friends and then another when we're talking on the job to coworkers. In situations involving lawyers & judges we communicate formally. The choice of terms, that mean the same thing simply, depends on who it is that's being spoken to. As far as what they mean, Albeit and although mean the same thing, howbeit and however... same thing