SO, as far as I understand, lysosomal hydrolyzing enzymes are first synthesized as proteins in rough ER and then they are budded off from the ER. The vesicles containing those proteins reach cis golgi and then they are properly folded to proper hydrolyzing enzyme but they are tagged with mannose-6-phosphate at this point, so they font have the ability to hydrolyze molecules just yet. In the mean time, some molecules can be engulfed by the cell and and these enter the cell as a membrane bound vesicle (endosome) containing proton pumps in its membrane which maintains an acidic environment inside the vesicle (which matures to late endosome). Vesicles containing hydrolyzing enzymes now move to those late endosomes and fuse with them. The low pH cleaves the mannose-6-phosphate tag from the enzymes and they become functional thus late endozome matures to lysosome.
The definition of primary lysosome says it is that lysosome that directly buds off from the golgi bodies and secondary lysosome is that lysosome which gets formed when primary lysosome binds with a vesicle and hydrolyse its content.
So are primary lysosme and those vesicles same?