Where is that woman that's supposed to teach me how to ride a Chocobo in Calm Lands?

[Tavrobel]

no. in the top left corner of the calm lands (behind the agency and to the left) is where she is, there is also an al bhed primer and a rap which leads to tidus' celestial weapon, but u cant get it just yet

The position from which the Trainer is changes depend from point of entry.

I saw a Chocobo rider near the right side of the Calm Lands, but she just kept telling me that smart riders use chocobos. Is that the same person?

No. The Trainer gives you a list of options right away. Although, I', starting to have my doubts about the accuracy of Arena/Mt. Gagazet locations, not because of your statement, but because if you entered the Arena/Remiem, it is still the Clam Lands, so therefore, it would probably leave the Trainer in the Center, because you probably use a Chocobo to get to both areas (the Arena is PURE convience, not at all necessary). I will have to check.

UPDATE:
If you enter from Macalania, the location of the Trainer is still on the first cliff, instantly noticed.
If you enter from Mt. Gagazet/Cavern of the Stolen Fayth, the Trainer is sitting on a small ledge that is easily seen from the entrance.
If you enter from Remiem or the Arena, the game saves your Chocobo's location, so the location of the Trainer is the same as when you entered those areas previously. (So if by Airship, she is in the Center, if by Gagazet, the Gagazet exit, and if by Macalania, then by Macalania).