difference between bicubic filter and bicubic interpolation on regular grid/bitmap

In 2d is there a difference mathematically between a multivariate
bilcubic (or bilinear, sinc etc) 'interpolation' and  the 'filter'
expression of the same name  ?

- For example taking the multivariate bicubic 'interpolation'
expressed on the wikipedia page:
http://en.wikipedia.org/wiki/Bicubic

In comparison with a bicubic 'filter' using a weighted sum of values
in a sub-grid:
http://mi.eng.cam.ac.uk/~twd20/libcvdhtml/image__interpolate_8h-source.html
eg where w = (  pow(p(x+2), 3) - 4 * pow(p(x+1),3) + 6 * pow(p(x), 3)
- 4* pow(p(x-1),3))/6;

If i plug values in from a regular grid can i expect the same results
from each algorithm. the filter notation appears a lot simpler and
appears to have a lower computational complexity.

I understand and apologise for what is probably a basic question but i
dont have the math to show/derive this myself.