They had a little fun with the names back when they were pushing the whole "hd" thing. It doesn't really mean much. Just look at the version number and it will tell you which one is the newest one.
The other machine has both because they downloaded it, or they installed iLife 08 over iLife 06. Doing that keeps both versions.
The difference:
06 is more of a traditional Movie making program, with a timeline, etc. 06 is generally preferred by people with movie editing experience. 06 offers finer controls and more transitions than the newer version.
08 is a combination cataloging/editing program. Like iPhoto has Events and Albums, iMovie 08 has raw footage and projects. iMovie is much easier to learn for someone who has never done any editing. It can also be easier to create compilation videos from a wide variety of footage shot over the years.
iMovie 08 isn't horribly different than the old way of editing videos though and the pervious versions of iMovie never really handled that editing style horribly well (FCE was much better).
thank you for all of your help and thats cool that i can download imovie 06 because thats what i use at school and not even my teacher knew the difference between hd and regular imovie