Uhm... Not sure if the answers were explicit enough. I know I'm being pedantic. Bare with me.
C41 is color chemistry (1 hour photo lab, as mentioned previously). Ilford XP2 and Fuji Neopan 400CN are examples of black and white film which is developed in C-41 chemistry.
All other films that are black and white may be developed using a variety of developers. The most common of which are D-76 (kodak) or ID-11 (Ilford). Check the massive dev chart for developing times on your particular film.
As for what the the shop owner said / what you bought: If the Ilford film is HP5 or Delta 400 (these are the ISO 400 traditional films that Ilford makes), they cannot be developed in color chemistry. If it is XP2, it can.
There are a ton of other options on the market, but many stores do not carry a variety of film. Some brands which make traditional B&W films: Kodak, Ilford, Fuji (although they might have stopped -- I am not following them since the latest market abandonment), Foma, Efke, Rollei, Adox... Some of these might be the same film under different labels, but film is being produced in America, England, Japan, China, Croatia and the Czech Republic. Probably others.
Unfortunately, the same cannot be said about color (C-41 negative or E-6 slide) film. quality film using those standard chemistries are only produced in the US and Japan (Kodak and Fuji).