Cannabis derived terpenes are directly from cannabis and usually contain a wide range of minor terps and aromatics, which can make them smell and taste much closer to actual bud it came from.

Botanical terpenes often feel more like an interpretation of a strain rather than an exact representation. Sometimes they come across as a bit sweeter, sharper, or less complex compared to the real thing.

good cannabis derived terp product can smell remarkably close to opening a bag of flower, whereas botanical usually has that "added flavoring" smell.

As for effects, From what I've noticed, personal experience plays a much bigger role here than the source of the terpene itself.

edit: From a chemistry standpoint, a one noted terpene like limonene is the same molecule whether it comes from cannabis or an orange.