Yeah, the names are screwy. Most people seem to refer to them as iMovie 06 and iMovie 08. The "HD" one is the older ("06").
Since you own 08, you can also
download a free copy of 06.
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.