Effectively yes. Sometimes it's not quite "open core" in the sense that they don't offer two versions of the same piece of software, but rather separate program

Effectively yes. Sometimes it's not quite "open core" in the sense that they don't offer two versions of the same piece of software, but rather separate programs that are meant to work in conjunction with that software (or a paid cloud version of the local program), but the end result is similar. There is some nuance in how this affects community uptake of the software if it is divorced at the software level.