Basically, yes. The Arduino core / framework are the pieces of code that implement the Arduino APIs like digitalWrite() etc and give the basis for all Arduino libraries. You can e.g. inspect the core implementation for AVR here.
The post Frameworks, platforms, and boards, oh my! has some more in-depth info.
You can only use one Arduino core implementation, as it will be conflicinting with another core implementation regarding the implementation of functions if you put another one in there. There exists however one very special case where two frameworks can be used apparanently simultaneously, which is because one is actually the basis of another. That framework = espidf, arduino case for ESP32’s is also mentioned in the last post. For all others, you can only choose one framework.