As we saw elsehwere, in his "Über Sinn und Bedeutung" (1892), Frege introduces an unusual, and indeed inadequate definition of the term "Bedeutung" ('meaning'). According to this definition, the term "Bedeutung" applies to what an expression refers to (rather than, as would be correct, to an expression's meaning).

Frege's article had exceedingly strong influence on the meaning-theoretical thinking of early analytic philosophers such as Russell, the early Wittgenstein, Carnap and Quine. Along with this influence, Frege's inadequate definition of the term "Bedeutung" spread out, and started causing confusion, misunderstanding, and talk at cross purposes. One fine example of an extended, detailed and perfectly irrelevant discussion sparked by Frege's terminological mistake can be found in Davidson's famous article "Truth and Meaning" (1967). 

In this text, Davidson at length discusses a theory which is introduced as follows: 

It is conceded by most philosophers of language [...] that a satisfactory theory of meaning must give an account of how the meanings of sentences depend upon the meanings of words.[...] One proposal is to begin by assigning some entity as meaning to each word (or other significant syntactical feature) of the sentence; thus we might assign Theaetetus to 'Theaetetus' and the property of flying to 'flies' in the sentence 'Theaetetus flies'. The problem then arises how the meaning of the sentence is generated from these meanings. Viewing concatenation as a significant piece of syntax, we may assign to it the relation of participating in or instantiating; however, it is obvious that we have here the start of an infinite regress. Frege sought to avoid the regress by saying that the entities corresponding to predicates (for example) are 'unsaturated' or 'incomplete' in contrast to the entities that correspond to names, but this doctrine seems to label a difficulty rather than solve it. (Davidson 1967, 304)

Clearly, theory Davidson describes here views the meaning of an expression as this expression's extension. And clearly, too, Davidson believes that this is Frege approach to the meaning of an expression.

He now starts a rather lengthy and highly sophisticated discussion of this 'Fregean' approach, developing it in various ways, only in order to reject the whole approach in the end. The argument he refers to is rather sophisticated, too, and is connected with the real problem at most indirectly, if at all. Had Davidson concentrated on the matter itself (rather than on Frege, as a philosophical celebrity), he might easily have found a much more pertinent argument: the equation of the extension of an expression with its meaning is simply inadequate.

Apart from this, Frege never did subscribe to this 'extensional' account of meaning Davidson ascribes to him, as we saw. Davidson's belief that he did is based on a crude interpretatory mistake. But of course, although Frege never subscribed to such a theory, he is partly respondible for that mistake. Because he provoked it by using for the extension of an expression, quite inadequately, the term "Bedeutung".