What is the difference between abundance and dominance in an ecosystem?
There is a difference between dominance and abundance in vegetation science, and your citation is about vegetation.

Abundance is the relative representation of a species in a particular ecosystem. It is usually measured as the number of individuals found per sample. 

Ecological dominance is the degree to which a taxon is more numerous than its competitors in an ecological community, or makes up more of the biomass. 

In vegetation science, abundance is usually measured as the number of individuals or the percentage of coverage of that species in a plot. An abundant species would typically have a lot of individuals in the plot. A dominant species dominates the other species, so typically covers more than 50% (up to 100%) of the plot. Doing this, it also takes away space (and light!) for other plants.
Usually abundant species also cover a lot, but small species (for example grasses) can be abundant without becoming dominant while large species (like trees) can be dominant with relatively few individuals.