Hi David
I use both Aperture and Lightroom, vacillating between the two depending on which is peeing me off most this week.
Basically,
Aperture - Lightroom
Library - Catalogue
Project - (Filesystem) Folder or Collection (see below)
Album - Collection
Smart Album - Smart Collection
There's no direct equivalent of an Aperture folder in Lightroom, except at the filesystem level. So your Aperture projects for 2013 may be in an overarching folder called "2013" and in the same way, LR can have a 2013 folder but that LR folder will be visible in your Finder/Explorer whereas Aperture folders are found only within Aperture.
There's no reason, btw, why you can't organise LR according to "projects", it's just that most LR users seem to use the year-month ±day (filesystem folder) paradigm which is reflected directly in their LR folders. Incidentally, that's why files should only be moved within LR rather than through the Finder/Explorer. But if you wanted to, you could import into LR according to "project". I'm sure some do, too, especially wedding shooters.
Another thing (that you're probably aware of) is that LR catalogues are completely referenced in nature, whereas Aperture libraries can be either managed or referenced. Of course, if you name your Aperture Projects by year/month in a referenced manner, then it's basically the same setup as LR using date hierarchy folders.
Hwyl fawr