Is ivy (genus Hedera) a shrub or an herb? It seems like the difference between a bush (shurb) and an herb is that a bush has a woody stem. What does that make ivy (genus Hedera)? I know that ivy can get a pretty hard stem, does that count as woody? Is there something between a bush and an herb?

Woody plants are usually either trees, shrubs, or lianas. Ivies are lianas, they can have 40 years of woody growth rings and bark. The categories are flexible. It's an arbitrary division for convenience, it isn't that clear cut. Bamboos for example, are a woody grass.

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Does that count as a woody plant? yes it's a woody liana.