As a bespoke maker, if I charge for design drawings and get paid for them does the design then belong to the client?

The basic rule is the IP is owned by the person who creates a design unless you have completed an agreement that assigns the rights to somebody else. If there is no assignment, the client has the right to use the design for the purpose for which it was intended but they don’t own the IP. But if someone copied the design your client would not have the rights they needed to stop the copies.