In modern parlance we talk about two different speeds of light in general relativity. We distinguish between the local speed of light, which is always $c$, and the coordinate speed of light, which can have any value from zero upwards without limit.
In Einstein's early papers he simply refers to the speed of light and by this he means what we would today call the coordinate speed of light. I'm curious to know if at any point in his published work he started making the same distinction that we do today, and if so whether he used the modern terminology.
I've attempted to investigate this using the Einstein Digital Archive, but with 5,000 documents it's proving a bit impenetrable. I wonder if someone more familiar with Einstein's key papers would be able to answer this more easily.
If it is of interest there is a related question in the Physics Stack Exchange: GR. Einstein's 1911 Paper: On the Influence of Gravitation on the Propagation of Light