We see in the market that a implied volatility surface is not flat. Based on this observation different models were developed to capture the structure, e.g. CEV / SABR. 

A measure often used for the skew is a risk reversal, i.e.

$$\sigma\_{25,c}-\sigma\_{25,p}$$

and butterfly

$$\frac{\sigma\_{25,c}+\sigma\_{25,p}}{2}-\sigma\_{ATM}$$

where $\sigma\_{25,c}$ is the implied volatility of $25$ delta call. 

Looking at the skew, you are interested in the slope an curvature. The mathematical objects would be for the slope of a function $f$:

$$\frac{f(x+h)-f(x)}{h}$$

and for the curvature

$$\frac{f(x+h)-2f(x)+f(x-h)}{h^2}$$

So why are the above measure (RR and BF) not constructed like this? Should they be seen as an approximation?

Moreover, why is it common to just look at a specific RR / BF, 25 for example. Wouldn't it be more reasonable to calculate these measure for every strike (in delta measured) on the grid? Obviously the slope and curvature can change as for different deltas.