In addition to the two aspects of the past tense that you mentioned, I’ll also speak about the imperfect, since it is also indispensable. They each have various denominations, depending on region and what distinctions you have in mind in naming the tenses:

(Examples in first person singular)
comí: pretérito indefinido, pretérito perfecto simple, pretérito, pretérito I

he comido: pretérito perfecto compuesto, presente perfecto

comía: (pretérito) imperfecto, pretérito II

Simple refers to the fact the no auxiliary verb is used, just the main verb. Compuesto (compound) means that an auxiliary is used to form the tense.

Aspect:
Perfecto means the action is thought of as having been completed before now (or another time), but with a connection to now (or the time in question). Imperfect means that the action is thought of as not completed (even though it may have been completed). You have a similar distinction in Russian as well, where you have perfective and imperfective verbs. Indefinido (indefinite) is a term used — mainly in European Spanish — to refer to the pretérito simple meaning neither perfect nor imperfect. This has to do with the fact that the compound form is used a lot more in peninsular Spanish than in Latin American Spanish. For example, Spaniards almost always say “he combed” rather than “comp” when referring to something they did (or have done) today, even if they specify an exact time. On the other hand, many Latin Americans avoid using the compound form, even for something that happened a minute ago. Note: Southern Spain, the Canary Islands, and the Caribbean generally fall in between European and Latin American usage on this point.

Quise decir "los españoles casi siempre dicen he comido en vez de comí cuando se están refiriéndo a algo que hicieron /han hecho hoy."