Is there a difference between the Hendaya and the Irun-Hendaya stations?

Maybe this will help: http://en.wikipedia.org/wiki/Irunrailwaystation. When we went from San Sebastian to Sarlat, the switch from the Eusko Tren was just about walking across a paved lot. Irun is a stop along the Eusko Tren. The Wikipedia article lists several train options to Burgos. All seem to go through San Sebastian. There are lots of good links for further exploration.

This map -- https://www.google.es/maps/place/Ir%C3%BAn,+Guip%C3%BAzcoa/@43.34709,-1.780558,14z/data=!4m2!3m1!1s0xd51088ba8674817:0x86ff9f9180d14bb8 -- should give you an idea of how close they are. I hope the link works.

When I Googled "irun hendaye transfer" I got lots of links about this somewhat strange set up due to the change in the gauge of the tracks. Some say, and the map seems to indicate that you could walk. Some say there is a bus. Some say to use the Eusko Tren. According to this schedule from their website -- http://www.euskotren.es/sites/www2.euskotren.es/files/docs/horarios/H5%20-%20Zumaia-Hendaia.pdf -- it appears to take about 5 minutes between Irun and Hendaye.

Thank you Lo--that's very helpful!

It's simple - you change trains in Irun by walking just metres across a platform.

They are separate stations and not all trains stop at both. Train schedules online are the best way to identify transfer points, at least on the national railways. From Bayonne to Burgos, DB reflects 2- 3 departures per day with one connection at Irun station, which is the end of the line for the French train. The Spanish train that you need to connect to Burgos doesn't run across the border to Hendaye, so don't plan to get off there. (If your destination were San Sebastian, for instance, then you could catch the local Eusko train from either station.)

Thank you Neil and Laura!

Thanks for the thanks.