Article with 'client'

I am talking about our business billing clients (the process) Can I infer that either article can be used depending on which I mean?

#1---- Let's say you create a bill and send it to the client. (no client has been previously mentioned, but I use the definite article because there's conceivably only one client for that bill).

#2---- A bill that is sent to a client should be stamped. (Here no client has been mentioned as well, but I mean that a bill that is sent to any client).