Does DVI support 1080p?

So I've done some research and it appears there are 2, maybe 3 different types of DVI, the three being DVI-A, DVI-I, and DVI-D and apparently the DVI-D supports 1080p but I am unsure of whether my MacBook supports that. I have a late 2008/early 2009 model of the 13" aluminum MacBook. It has a mini display port as I'm sure you all know. My current setup is using the apple mini display port to DVI adapter and then I'm running a DVI cable (the one that came with my external monitor) to a 23" Samsung 1080p LED monitor. I know I am running my monitor at 1920x1080 resolution, but my question is am I losing quality with DVI as opposed to HDMI?

Message was edited by: msq882006