What's the difference between morphospace expansion and packing?
You're almost there--both terms concern the relationship between increases in species richness and morphological diversification. They're two opposing patterns:

Morphospace expansion indicates that a lineage is occupying new areas of morphospace with increasing species richness. (The slope is more or less relating density of morphospace occupation to speciation rate--so > 0 means new species tend to go farther away in morphospace.) 

Morphospace packing indicates that a lineage is not expanding its morphospace with increasing species richness, so the existing region of morphospace that it occupies is getting more densely filled, instead of expanding. 

The relationship between functional/ecological diversity and morphological diversity isn't always clear cut, though, so you have to be careful when relating the two. If you're going to use these concepts, especially if you're going to use morphological diversity as a proxy for functional diversity, it's best to state that assumption outright. 

This paper includes a nice discussion of the two concepts (and is cited by the one you list): http://rspb.royalsocietypublishing.org/content/283/1822/20152013