How is a 1-foliolate leaf (e.g., Hardenbergia) different from a simple leaf?
Look for a pulvinus at the leaf-stalk/leaf-lamina junction.
So from a strictly anatomical identification standpoint, this can be a bit confusing.
According to "Plant Identification Terminology: An Illustrated Glossary" (Harris & Harris, 2001):
Simple: Undivided, as a leaf blade which is not separated into leaflets.
Leaflet: A division of a compound leaf
Compound Leaf: A leaf separated into two or more distinct leaflets.
So the definition of a compound leaf is to have "two or more distinct" leaflets.
one-foliolate (1-foliolate, unifoliolate): a compound leaf reduced to a single leaflet, usually recognized by the articulated or jointed ‘petiole’, which is in fact a petiole plus a petiolule.
So what gives?
Perhaps this is due to a deficiency in terminology, as discussed (and corrected) by Jiménez-Saa 2011.
But, again Harris & Harris (2001) hint toward how this might arise [emphasis mine]:
Unifoliolate: a leaf theoretically compound, though only expressing as a single leaflet and appearing simple.
So there is still a fundamental difference between the two.
Structurally, we can see the difference at the basal joint of the foliar structure:
Simple or unifoliolate: The leaf is undivided...with (unifoliolate) or without (simple) an articulation between the leaf lamina and leaf stalk. [source]
Unifoliolate leaf is usually recognized from a simple leaf by the presence of a distinct joint or a pulvinus at the lamina-petiole junction, which is in fact a petiole plus a petiolule.
- Note: Pulvinus = a distinct enlargement/swelling at the base of (sometimes at the apex of) a petiole or of a petiolule.
Note: a discussion about the developmental evolution of unifoliolate characteristics in Cercis canadensis is discussed here.