Yup - all direct injection or IDI compression ignition engines are diesels no matter whay they burn or what you call them..

I don't think there is any diesel that is constant pressure. I know people have tryed to do it.. There is no reason for that now days anyway. I'd say that all modern diesels ignite the fuel before top dead center and that causes a pressure spike that works well with the power stroke. The knock you hear in a diesel is a pressure spike.

There are plenty of IDI (inderect injection as in a pre chamber ) diesels out there as well.

Our little engines don't fit any catagory perfectly except internal combustion. But the compression ingnition part makes it fit the diesel catagory best in my opinoion.