I don't care what you call the insurance. Call it trip, diving or bunny rabbit, it doesn't matter. I only concern myself with the coverage/benefits.
The definitions are important. What is covered is the issue.
As a general rule, normal holiday (trip) insurance have very limited coverage for scuba diving. Most underwriters are ignorant on diving matters, at least in my limited experience. If insures can avoid paying out, they will.
In the past, I have had holiday insurance that would cover me for a 'try dive', or 'dive experience' with an instructor. But not as a diver.
I learnt to dive on holiday, as part of the course, we where required to have a specific insurance, because general holiday insurance was unlikely to provide sufficient coverage. It was a requirement to protect both student, and the school.
Another issue, this is an international site, so there are often noticeable differences between countries or territories. DAN are a good example, DAN Europe have different policies and restrictions to DAN USA (as someone has already pointed out). My Amex card is similar, I know my American friend has a totally different set of benefits with the 'same card' that I have with mine - especially around insurance!
I seldom dive with a guide, and hold a number of diving qualifications.
I am very aware that there are a number of people who find their 'all inclusive' travel insurance is anything but, when involved in a diving accident, a similar issue also arise for other sports. Therefore, for diving holidays I ensure I have a policy specifically provided by a diving insurance specialist. My sister does something similar with her riding holidays, although horse riding is far more dangerous than diving.