Here are the definitions of connectives and conjunctions taken from the NLS 1998
A word used to link clauses within a sentence. For example, in the following sentences, but and if are conjunctions:
It was raining but it wasn’t cold.
We won’t go out if the weather’s bad.
There are two kinds of conjunction:
a. Co-ordinating conjunctions (and, but, or and so). These join (and are placed between) two clauses of equal weight.
Do you want to go now or shall we wait a bit longer?
And, but and or are also used to join words or phrases within a clause.
b. Subordinating conjunctions (eg when, while, before, after, since, until, if, because, although, that). These go at the beginning of a subordinate clause:
We were hungry because we hadn’t eaten all day.
Although we’d had plenty to eat, we were still hungry.
We were hungry when we got home.
A connective is a word or phrase that links clauses or sentences. Connectives can be conjunctions (eg but, when, because) or connecting adverbs (eg however, then, therefore).
Connecting adverbs (and adverbial phrases and clauses) maintain the cohesion of a text in several basic ways, including:
addition: also, furthermore, moreover
opposition: however, nevertheless, on the other hand
reinforcing: besides, anyway, after all
explaining: for example, in other words, that is to say
listing: first(ly), first of all, finally
indicating result: therefore, consequently, as a result
indicating time: just then, meanwhile, later
Commas are often used to mark off connecting adverbs or adverbial phrases or clauses:
First of all, I want to say …
I didn’t think much of the film. Helen, on the other hand, enjoyed it.
Connecting adverbs and conjunctions function differently. Conjunctions (like but and although) join clauses
within a sentence. Connecting adverbs (like however) connect ideas but the clauses remain separate
I was angry but I didn’t say anything. (but is a conjunction - one sentence)
Although I was angry, I didn’t say anything. (although is a conjunction - one sentence)
I was angry. However, I didn’t say anything. (however is an adverb - two sentences)