Most languages have a fluid vocabulary. A word can mean something in one year and -- in another year or ten years or fifty years -- have a different meaning. Sometimes the meaning can even flip; a "good" word can become a "bad" word. Some languages, such as French, have monitoring organizations to attempt to control the language. Of course, people will use language as they will no matter what the dictionary says.
When my business partner and I had our company, one of my many hats was as head of client support. This was quite apart from customer support. Most of our clients included repeat business over a span of ten to fifteen years. We did not want to sell them something that would fill our pockets but not meet their needs. I like to think that this was, at least in part, because of our desire to do "the right thing", but it was also looking at the relationship from a long-term point of view. A client, for whom we did our best, became a referring client and a long-term, repeating, client.
We had an excellent percentage of repeat business -- around 90% of our clients either referred some other company to us or purchased more products at a later time. And, within the world of software, people that we worked with at one company often moved to another company and, when need arose, they thought of us to supply their needs.
This did not always work out, of course. We had clients who "disappeared". They had problems and, instead of reaching back out so we could work with them to eliminate the problems, they huddled together and failed. I'm sure that we all know both individuals and companies who take this path. In one case, this happened but it happened deliberately because they wanted a scapegoat for poor product decisions that they had made.
90% is still a good record for a company. But what about customers? Would treating them as customers have really made a difference? It depends. If a person uses both words as largely synonymous then there is no difference. But if a customer is a one-time transaction and a client is an ongoing relationship then there is definitely a difference.
More than thirty years after having co-founded the company, I am still in touch with some of our client companies and people who have worked with them. We are no longer actively supplying product -- but we can still offer suggestions, and advice, when asked.
There have been no regrets that we approached each company as a client.