Both of your definitions are too restrictive.
Even in the US, the term "adjunct professor" is used in at least two ways. The older meaning was for an extra appointment to a department for someone employed in another department or another institution. This meaning is still in use at some institutions, with "Adjunct Associate Professor" reserved for those with a regular position elsewhere. Such a position might involve no classroom teaching and no pay, for example, and just be there to allow this person to advise graduate students.
The newer meaning is a euphemism for part-time instructor. It is similar to calling a worker at a big box store an associate instead of a sales clerk. Words shift over time.
As to emeritus professors, there is no requirement that an emeritus professor teach, although many do. The rank of emeritus professor is somewhat formal, given to some retired professors, but it can be associated with certain rights. For example, the right to apply for a research grant, get an office, and if very lucky, a good parking sticker.
You need to know how these ranks are defined at a specific institution to make sense of what is happening. The dean might well have been a full professor at another institution and an unpaid adjunct full professor at the current one, then been hired as dean. Or not. It is hard to say. I would look at this person's CV to get a sense of what they have done over the years.