The q-Pochhammer symbol (for $k>0$): $(a;q)_k = \prod\limits_{j=0}^{k-1}\left(1-aq^j\right)$
The Pochhammer symbol / rising factorial: $(a)_k = \prod\limits_{j=0}^{k-1}(a+j)$
The falling factorial (sometimes identified with the Pochhammer symbol instead of the above): $a^\underline{n} = \prod\limits_{j=0}^{k-1}(a-j)$
The q-Pochhammer symbol is supposedly the q-analog of the Pochhammer symbol, meaning if we set $q=1$, we get the Pochhammer symbol. Wolfram MathWorld makes this claim, as does Wikipedia and this very site. Yet it it clearly false. For example, $(3;1)_2 = 4$ whereas $(3)_2 = 12$ and $3^\underline{2} = 6$. So we have an inappropriate name ("q-Pochhammer symbol", which suggests it is a q-analog) and a clearly false statement (that it is indeed a q-analog), both apparently widespread and generally accepted. What's going on here?