Use customers and users to distinguish between the two categories. Those that pay for your service are customers. Those that use your service are users. Note that a customer can also be a user, but it doesn't always have to be the case. For example, if you are developing children's software, your customer is the parent, and your user is the child. On the other hand, if you are developing tax software, your customer is also your user.
I would say that the terms consumer and client are similar to the term user, in the sense that they do not necessarily identify the individual as a paying customer, but I think all three have slightly different connotations.
The term client is mostly used to identify those individuals obtaining services from a professional, and who have somewhat of an on-going relationship with that professional. For example individuals obtaining services from a lawyer, an accountant, a web designer. This can be paid or unpaid. For example, some lawyers do pro bono work, but still refer to the individual they are representing as a client.
A the term consumer is usually used to identify someone who consumes or uses something. This something is usually a product, but it can be a service as well. Consumer usually refers to a paying individual, but I don't think it necessarily has to be the case. The Legal Dictionary of Dictionary.com defines a consumer as, "one that utilizes economic goods; specifically: an individual who purchases goods for personal use as distinguished from commercial use". The big discriminator here seems to be the distinction between personal and commercial use.