The (simplified) sequence (in the US) was:
ARPANet (1969 - 1990)
"Commercial Internet" (1989 -)
NSFNet (1990 - 1996)
Internet2 (1996 -)
NSFNet, overseen and partially funded by (unsurprisingly) the National Science Foundation, had quite a number of restrictions and an acceptable use policy that prohibited commercial use. To get around those restrictions, the "Commercial Internet Exchange" was formed allowing commercial networks to easily interconnect.
As for "apps", the World Wide Web was invented in 1989 and publicly released in 1993. Prior to that, there was "Usenet News" and a service called "gopher". There were many centralized services that interconnected with "the Internet" (mostly NSFNet), e.g., Compuserve, AOL, MSN, etc.