There's also an 'Enlace' train and that will require a change of trains in Baeza. It makes a dozen plus stops, so you should avoid it.
If you are traveling in the next few months, consider buying your tickets online in advance. Web-discounted fares are about 28 euros vs the full fare of 41 euros. Tickets are currently available up to Dec. 15.
I'll only add that if you have any problems with using renfe.com, simply use either www.petrabax.com/renfe or www.raileurope-world.com, both of which have a direct link to the Renfe ticketing system so charge the same prices, including web and estrella fares, with just a small mark-up in the case of Petrabax, a €4 fee in the case of Raileurope-world (not to be confused with any other of Rail Europ's various websites, as not all of them have this link)
I bought our train tickets about 60 days out and had no problems on the renfe site getting the web discount. After reading all the comments I was very concerned but my transaction went smoothly. I did call my credit card in advance. That may have helped.
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