It matters because the split is where the money and the risk live. A clear division — the MSP owns patching, monitoring and after-hours response while internal staff own applications and user support, say — is billable and defensible. An unclear one means both sides assume the other is handling something, and the gap is discovered during an incident.
The common misunderstanding is treating co-managed as a discount version of fully managed. It is a different service with different economics: fewer endpoints under exclusive control, more coordination overhead, and a client who can evaluate your work in detail. Priced as a discount, it usually loses money.