They're tagged through cartridge, and the tags aren't big. Same shit as a human wearing earrings. I'm sure getting your ears pierced sucks, but I'm sure sharks face lots of things in their lives that suck.
They also surgically implant small tags in salmon and other migratory fish for tracking. They do this shit because in rivers like the Sacramento in California, there's so much damming and hydro plants and shit going on they've pretty much fucked up upstream fish migration. So they try building salmon ladders and fish fences and other stuff to help direct fish upstream, and modify hydro dams or install fish bypasses to try to increase the chances of fish making it through them alive... and tagging/tracking fish ensures that they work.
Another study I recently read about is that fish are attracted to warm water when they're migrating upstream, so if you've got a coal/nuclear/whatever power plant dumping cooling water into the river, fish will hang out around the power plant outlet all confused instead of migrating, and it can result in massive fish kills. To prevent this from happening they have to idle the power plants during fish migration time, or switch to using cooling towers.