BuddyPress.org

“Am I crazy to try to build a site on this foundation where I anticipate high levels of users? “
There’s nothing wrong with building a site on WP/BP, it all depends on your server. You could start with shared hosting, but once it gets to a certain number of sub-blogs (around 300 or so) you would need to go multiple DB and upgrade to dedicated hosting.

“And, attached to the above, what is the difference between buddypress and buddypress MU?”
There’s only one BuddyPress plugin. And this plugin can be installed in either main site or one of sub-blogs at this time although you can enable multisite mode which is not the same as having several instances of BuddyPress in one installation. Perhaps you mean BuddyPress installed in WPMU, which as noted above works mainly in the main site or subsite.