You are right in that it's just semantics.
When you see "Member" it's a dimension field. When you see "Value" it's a Measure field. Others are specific to the options on your filter, such as "Range".
When it lists out the individual items versus X of N, it's just if there's space (within some character limit, somewhere around 50 I'm guessing) where it represents them explicitily if there's space, but if you have enough selected, it shortens the message for readability.
It switches to Exclude, if that can be represented specifically within that character limit.
Not sure what prompts the "Many" nomenclature, but it may be when you use a condition or Top filter and the exact number is not known, or is dynamic.