Médico/a y Doctor/a

Médico/a y Doctor/a
 

Correct.

ok. I just realized laepelba made one too

Yes, the distinction between médico and doctor is correct. With the word "médico" is is almost always "el médico" or "la médico" depending on gender. "la médica" is not used as far as I know.

La médica is allowed:

médico, ca.
(Del lat. medĭcus).

1. adj. Perteneciente o relativo a la medicina.

2. m. y f. Persona legalmente autorizada para profesar y ejercer la medicina. MORF. U. t. la forma en m. para designar el f.

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In Central America, they always mixed the two. I actually believe I heard doctor more than I heard médico.

Ese charco no deja de darnos quebraderos de cabeza...

Supongo que Doctor sea el título de un médico. ¿Verdad?:thinking::o

We use them indistinctly, but is a little more popular to use it has María said.

If you think it, it isn't irrational:
Médico is the one related to medicine, one that can practice it;
Doctor is the one who has the title, so, is related to the medicine and can practice it too:
"Voy al médico" (a very little more used) - "Voy al doctor"
"Vino el doctor" (a very little more used) - "Vino el médico"

In my opinion both mean the same, it´s a question of register, Doctor being more posh!

Good to know. Common usage (in Mexico at least) seems to be "la médico", not "la médica", as far as I can tell.

We have to take in account that "Doctor" is more general too, a lawyer can be called Doctor (for me this is wrong), and after doing reserch you can obtain "El Doctorado", and you'll be a Doctor too.
"Doctor [en Filosofía.]"
So, saying "mi hermano es un Doctor" isn't too precisely.

An adjetive that is related:
docto/a
1. adj. Que a fuerza de estudios ha adquirido más conocimientos que los comunes u ordinarios. U. t. c. s.

P.S: here if it's a woman, la médica.