Google says Clientele means: "clients collectively." But so does Clients mean
You are correct that the distinction is very subtle and not easily discerned from a simple dictionary definition. Clients is the plural of client, and clientele refers to a body clients, per Merriam-Webster.
The tiny difference must be derived from experience and familiarity with usage, then. Consider:
We must find a way to make our clients more comfortable with the user interface.
Tom and Joe are two of our oldest clients.
As opposed to:
This store tends to serve a more up-scale clientele.
How can we appeal more to the youth clientele?
I argue that clients is used for a more concrete subject, to actual persons or entities that purchase and use goods and services. Clientele on the other hand, is used more abstractly, to refer to a type or category. This is not a hard-and-fast rule, however.
Your firm may have lots of different clients, but you only cater/serve to international-clientèle. So, when you group a type of clients based on some parameter(s), you say them clientèle.
All your clients = Asian clientèle + African clientèle + American clientèle + European clientèle + ... + Middle Eastern clientèle etc.
Nice explanation given in this article:
When you become someone's client you pay for the services (or advice) that he/she provides you. When you go to a lawyer or an accountant you become his/her client.
The term "clientèle" is used to refer to all the clients of a professional organization or business. You are thinking of the clients as a group. A "clientèle" can be defined as a "collective body of clients". Here are a few examples.
1 The clientèle of my cousin's law firm consists of big corporations.
2 The new restaurant has a very fashionable clientèle.
3 This bank's clientèle includes some of the richest people in the city.