Until the last years, my knowledge was that the rechargeable analogue of the 1.5 V batteries have only 1.2 V. This greatly decreased their usability (many devices did not work well with 1.2 V).
The cause of this lower voltage was chemical and it was considered a hard limit until some years ago.
However, today there are a lot of 1.5 V rechargeable batteries (lithium or nickel-based). I experienced it as a new development, in the last few years. They seem to do what they state.
Sometimes they are going so far that they even have an USB connector to charge it, like this:
These batteries can be charged by USB (much more than 1.5 V), but they still give 1.5 V. Other batteries, without an USB connector, can be charged with 1.5 V. In all aspects they look like 1.5 V batteries, except that they look chargeable.
How do they work? Maybe they have some integrated DC-to-DC transformer circuitry?