Why is specific volume unchanged at Critical Point but can have a range of values of Triple Point?
The triple point is the temperature in which the three phases ( solid, liquid, gas) can coexist but each phase will have a different density. The critical point is the boundary between liquid and gas where the density of the two phases are equal and therefore, the volumes will be equal ( since V = mass/density). So 1 gram of liquid will occupy the same volume as 1 gram of gas at the critical point.
Because these two points are very different in kind:
The triple point is where three different phases meet. As such, you find all three different phases in the vicinity. And, when you do the experiment, you will have some of each phase. Each phase has its own density, so the specific volume of the three phases put together depends on their relative amounts.
The critical point is where a phase change line ends. It's the point where the two phases on either side of the line become equal. As such, you only have a single phase at the critical point, and thus only a single possible specific volume.