Poner vs Poder?

Question

Why is it pones but puedes? Both words start with "po."

Answer

Hola John
There are certain verbs that undergo vowel changes when they are conjugated in the present. These verbs aren't grouped depending on how they are written. It is random verbs. So these two verbs "poner" and "poder" both have stem-changes but different ones:
Poner (to put)
Yo pongo
Poder (to be able to)
Yo puedo
I hope this helped.
Inma

Answer

Maybe this will help me to understand this concept:

¿Me pongo un café por favor? Could I get a coffee please?

Picture pouring coffee on yourself.

¿Me pone un café por favor? Could you get me a coffee please?

Picture someone in a restaurant putting coffee in front of you.

Yes this seems different from how we would say this in English.

Question: Is this construct used in Latin American Spanish?