I have a question about the terminology for special values of L-functions. Is the following a correct description of standard usage:

Suppose L(s) is an L-function which satisfies a functional equation relating $s$ to $w+1-s$, where $w$ is the (motivic) weight. ADDED LATER: I am assuming the L-function is motivic, otherwise (please correct me if I am wrong) there is nothing special about the value at any integer.

1) If $m$ is an integer then $L(m)$ is a *special value* of
the L-function.

2) If $m$ is an integer and neither $m$ nor $w+1-m$ is a pole
of a $\Gamma$-factor of the L-function, then $m$ is a *critical point*
and $L(m)$ is a *critical value* of the L-function.

3) $L(\frac{w+1}{2})$ is the *central value* of the L-function.

4) If $\frac{w+1}{2}$ is not an integer, then the central value is not a special value.

I am pretty sure 2) is correct, unless Deligne's notion of critical point is not the only one. I am also pretty sure 3) is correct, since the central point of the functional equation is pretty unambiguous. It is 1) and 4) that I am hoping the experts can clarify.