Can one type of bacteria cause several diseases?
Yes, one type of bacteria can cause multiple diseases.  For example:

"Rheumatic fever is caused by group A Streptococcus. This bacterium causes strep throat or, in a small percentage of people, scarlet fever. It’s an inflammatory disorder." [https://www.healthline.com/health/rheumatic-fever#causes].  

The difference is in how the individual's immune system responds to the infection (and how the infection is treated).  Everyone responds a bit differently to the same infection.