At my university, we carry around sheet music in black folders in backpacks. I imagine this practice is not the same among professional musicians, such as those in an orchestra or a big band. How do professional musicians normally carry around music?
In the big band, a flight case holds all of the orchs, which get set up by the band leader or one of his minions, on the music stands on the bandstand/stage. That way, no-one ever forgets their music, or brings the wrong folder, and the dots never get lost.
For personal use, there is a special sort of leather case, which has a metal bar to close it over. Never found why it was designed like this, but musos still occasionally use one. 50 or so yrs ago, most musos would use one.
It is very typical for musicians to have a folder or binder for whatever sheet music they are using. It is also not uncommon nowadays to see musicians using and iPad or a tablet to store digital copies of their sheet music and using it in place of a binder or folder.