Enzymes are classified by function, not structure. Back to the questions from Harlan Bauer - Harlan asks specifically about the names protease, proteinase and peptidase. Note tho' that 'protease' is a recognised subclass of hydrolases which are enzymes involved the the hydrolytic elimination of a bond in protein. The mashing enzymes that we are most concerned with, the amylases, proteases and glucanases are classed as hydrolases - that is they catalyse the hydrolysis of bonds in amylose and proteins respectively. I believe that there are also some ligases involved in protein breakdown too.
Alpha amylase is an endo-amylase because it can act on interior bonds of a saccharide.
It'd be interesting to read more on this. Your question implied that certain proteases will only attack amide bonds in selective weight proteins. I don't believe that this is the case. I'm not aware of a significant molecular size contraint on the substrate for the proteases. As a ballpark figure, amino acids range from a molecular weight of 89 to 204 and probably average around 133 or so.