A number of apples means an indefinite quantity of apples, roughly equivalent to quite a few apples or several apples.
I have a number of apples in this bag.
The number of apples, however, means a definite quantity of apples: the exact number of apples under discussion.
The number of apples in this bag is seven.
In both, the article (a or the) refers to number, not to apples; but while a-number-of acts is a multiword quantifier which acts as a determiner on apples, the-number is a standalone noun phrase which is modified by the preposition phrase of apples.
Consequently, you cannot treat the two expressions as 'co-referential' like bare a and the, which can be used as determiners of the same entity at different stages of a discourse, because only one of them is used as a determiner. Thus, although these two pairs of statements work well enough:
I have an apple in this bag. okThe apple is a Red Delicious.
I have seven apples in this bag. okThe seven apples are all Red Delicious.
... this pair of statements is impossible:
I have a number of apples in this bag. ∗The number of apples are all Red Delicious.
If you want to do something like this, you have to use some other expression instead of a number of:
I have several apples in this bag. okThe several apples are all Red Delicious.
∗ marks an utterance as ungrammatical