No. The use of the word, "always" makes the answer either almost useless or it makes the answer require lots and lots of explanation. Please be stingy about using absolutes or all-encompassing words. There are so many ways and objectives to making amplifiers that, basically, there ain't no, "always".always assume
They are called, "current controlled voltage sources". They could have an amplified voltage as the output, and they might not. What you do with them determines whether they are voltage amplifiers.There are also devices that are CCVS (current controlled voltage source) that could have an amplified voltage as output. Are they also called voltage amplifiers?
The path from book learning to practical application has many avenues. This is a good site for exploring those avenues. You will get help here. Just try to avoid absolutes and try to keep your questions one at a time. Even a seemingly simple question can require a lot of explanation. A dozen questions in one post discourages attempts to answer you.