Hi Cupcake. Excuse my earlier dumb question about your route -- my eyes are blurry from looking at Spain trains on multiple websites and apps (involving Salamanca) for myself. I believe I see your problem and some potential solutions. As another post noted, there are no direct trains but the additional problem appears to be that Salamanca trains go to Madrid Chamartin while Madrid to Cordoba trains leave from Madrid Atoche so you have to change train stations in order to change trains. The Trainline app (a legit 3rd party with a small booking fee like Omio), shows a number of options at different times on Oct 16. You will need to add extra time to change stations and go through security at the 2nd station. Your train tickets should say that the ticket includes free ride on a Cercanias suburban/local train between stations. Because the trip is considered 2 different tickets, it says somewhere that if a train is late, its your problem. I paid a few dollars extra for the semi-flexible tickets.
The Renfe site doesn't seem to show trips that require a station change; it does not always even show all trips requiring a train change. Once you identify the legs you want, you can then find them on Renfe if you prefer it to Trainline.
There may be ways to avoid the station change if you are willing to make an extra train change but no station change. To find these, look for Salamanca to Madrid Atoche and Madrid Atoche to Cordoba OR Salamanca to Madrid Chamartin and Chamartin to Cordoba. It looks like there are some routes that have one additional simple within station change but you would need to explore.
Warning: You may see some routes on Iryo trains that are a train for one leg and a bus for the other leg, often taking much longer and not costing any less.
On Omio, I saw no train options shown but a number of buses. My guess is that the "good schedule" you saw on Omio might have been for bus because it switches without you knowing if it doesn't find trains.
