"Fusion" means that two things not only meet, but become completely mixed and intermingled so that they become a single substance in which you can no longer separate the two. "Convergence" means that two things are on paths that will result in their eventually meeting.
For example, "those two ships are on converging courses; if they don't change course, they will collide." However, it is (pretty much!) impossible for there to be a "fusion" of two ships.
"I bought a bag of ice at a convenience store, but I discovered that all the ice cubes in it had fused. I tried hitting the bag with my fist but I could not get them to separate."
"If a broken bone is properly set, the two pieces will fuse into one."
"When the celebrity walked into the party, all the guests started to converge on him."