Just saying the word "evolution" in a science discussion implies the theory of evolution. I have a feeling the person who claimed "there are 6 types of evolution" was certainly refering to the theory of evolution.
This is because if they did mean evolution in the general sense of the word then that makes their statement gibberish as it is the same as saying "there are 6 types of change". That doesn't make sense.
Because really there are as many types of evolution in the general sense as one choses to invent. For example we could use the term "glacial evolution" to describe how glaciers form and move, "volcanic evolution" to describe how volcanoes form, "orbital evolution" to describe how satellite orbits change over time, etc.
Just saying the word "evolution" in a science discussion implies the theory of evolution.
The problem is how we understand TOE. It is more than just Darwinian Evolution to modern scientists. Most scientists (and laymen) continue to use the simpler term “evolution” to
refer to both chemical and Darwinian evolution. As such, it is seen as a "unified theory" that knits together the fields of Biology, Physics, Chemistry, etc. For some, that is its attraction.