In France, the analogous institution was the Estates. Provincial estates had a long history, but the first Estates General was called by Philip IV to support him in his struggle with Pope Boniface VIII.
In Germany, the Imperial Diet served the emperors, while various of the German states had diets of their own. This was not hierarchical; that is, the regional diets were not necessarily tied to the imperial diet.
The analogous institution in Spain was the Cortes. These were strongest in Castile and Aragon, and it is long before there is anything like a national parliament for Spain.
The wide differences in terms reflect wide differences in the actual institutions. I refer you to Jensen and to Hay for discussion of how each of the national parliaments developed. What's important to note is that development differed greatly from one state to another. It was England where Parliament became strongest, though not until after our period.