Walk through the websites of a dozen regenerative clinics and you will see the two words used as though they were synonyms, or as though exosomes were simply a newer and therefore better version. Neither is accurate.
What a stem cell is
A stem cell is a living cell that can divide and can differentiate into other cell types. The ones used in this field are mesenchymal cells, typically sourced from perinatal tissue donated after birth. Once administered they remain metabolically active for a period, releasing signalling molecules that influence the tissue around them.
What an exosome is
Exosomes are small vesicles that cells release as part of normal signalling. They carry proteins and genetic material and act as messages between cells. They are not alive, do not divide and do not become anything else. An exosome preparation is, in effect, the signalling component without the cell that produced it.
Why you would choose one over the other
Because they are not alive, exosome preparations are simpler to handle and store, and the dose is more consistent from batch to batch. Because they are alive, cells continue producing signal over time rather than delivering it all at once.
Which is more appropriate depends on the tissue and the objective. In practice many protocols use both. What should worry you is a clinic that always recommends the more expensive option regardless of the case.
What the evidence supports
Research in both areas is active and incomplete. There is more published work on mesenchymal cells simply because they have been studied for longer. Exosome research is growing quickly but is younger, and claims about it frequently run ahead of the data.
The practical version
Ask which one your protocol uses, why that one was chosen for your case, and what it would cost with the alternative. If the reasoning is clinical you will get a clear answer. If it is commercial you will get an adjective.