Grout...that's the term for the groove fillings in between the tiles on the wall or flooring of the shower room.
Watching videos like the above, I bought from Home Depot: Simple Grout (Ready to Use), grout scraper/removal tool (triangular tip), and a float. The two bucket system (one clean, one for grout cleaning) sounds like a good idea.
Bulb seal is probably what the rubber seal around the door or doorframe of the shower. This one is a tough clean. Thus far, this article is the best I found online that has fixtures close enough to ours. It's perplexing figuring out how to remove/side off these seals.