Blu-ray vs hdmi

what should be the differences in the viewing experience between blu-ray disc and an HDMI feed directly from a macbook air (with thunderbolt to hdmi adapter). Assume, of course, the same display mechanism. Either at home on a 1080p pioneer tv or at a friends home with some home projection system that i have not seen yet.

Thanks

Also, am I correct that using a direct feed from my computer would be done by running the quicktime movie that FM creates? If not then, what?

Exporting to a bluray means, you a) need to export it as a HD movie b) you need to own a BD Burner and c) you need to burn it to a disk.
The advantage is: there will be no performance issues while playing back, e.g. because OS X might decide it wants to reindex your spotlight index. All you need is a BD player and your disk.
The downside is: Once you have exported and burned it, you need to re-export and re-burn in case you need to make changes. With a slideshow running directly from FotoMagico, you can pause and continue at any time.
When you connect your computer to a projector you can play it back fullscreen right inside FotoMagico, there is no need for exporting.

Because I do small videos for a bulletin board about 3 or 4 min max, I burn my HD movies on a bluray writer but on DVDRW’s yes just regular DVD’s you need Toast and blueray plugin. It plays fine in any blu-ray player but space is limited compared to blueray blanks. I hope this helps.