That is a good question, along with all the other different styles of knives. It seems like what I call one thing, everyone else calls another. I guess it is all in the eyes of the beholder. Then again, I don't claim to know a whole lot about knife designs, I just like to draw things up and build them.
Here is my interpretation as I am currently making one. I have drawn up two designs and have only built one. I envision a knife that is similar in style to a smaller fillet knife, but is more rigid. I shoot for smaller width of blade (edge to spine), a straight style of blade and the handle thinned out to be comfortable and light in the hand. Like stated before, I think of a slightly shrunk down, stiffer version of a fillet knife. I live in Colorado and smaller trout typically aren't filleted, like bass or crappie, etc. They are usually just gutted and heads removed. The one I designed has a long enough blade that a fish could be filleted if desired, but not as easily as with an actual fillet knife. As far as the bird part of it, I am not sure. Everything I have always hunted (doves, grouse, etc.) are usually just breasted. I can typically just do this with my fingers or with a little help of a pocket knife.
I have been using 1/8" stock for now. I have found HT'ing 1/8" with small widths can be tricky sometimes when it comes to warping. I would be interested in going a touch thinner, but I think it could be frustrating. I have snapped two blades right out of the quench (one trying to straighten some warpage, and the other one, well I don't really know why I tried to slightly flex it, but it didn't take much to snap it) Right now I am using O-1, so after an oven temper, I draw the spine even further to make it tougher, and it seems to have decent flex.
If this makes any sense, then hopefully you can design something practical. I have seen some that are small, and my next design will probably follow suit.