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When I run provider.backends(), ibmqx2 is listed as an available backend, but is not listed on the IBMQ systems page. This file from the archived repository ibmq-device-information associates backend name ibmqx2 with display name IBM Q 5 Yorktown. The IBMQ systems page does list a 5 qubit Yorktown device, but under the name ibmq_5_yorktown. This backend is also available via ibmq/open/main, but is not listed by provider.backends(). Are ibmqx2 and ibmq_5_yorktown respectively versions 1 and 2 of backend software providing access to a single Yorktown device? Or do these names refer to two distinct Yorktown devices?

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Actually, ibmqx2 and Yorktown are one quantum processor. When IBM Quantum platform was released, two processors - Yorktown and Tenerife were available. These processor were denoted also ibmqx2 and ibmqx4, respectivelly. Note that Tenerife processor is retired now.

If you have a look into IBM Quantum environment, you can see that there is ibmqx2 processor in list of available devices. See here:

enter image description here

When you click on ibmqx2, this page is shown:

enter image description here

So, it means that ibmqx2 and Yorktown are identical devices. The naming is just a legacy of former times.

I would be happy if anybody from IBM can add more comments.

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As @Martin Vesely answered, it is the same device.

Here is the README documentation showing that they are the same: https://github.com/Qiskit/ibmq-device-information/blob/master/backends/yorktown/V1/README.md

Here is a little screen shot of that documentation:

enter image description here

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