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If I wanted to ask someone to join me for breakfast, I might ask:

Have you had breakfast? (Swedish: Har du ätit frukost?)

And if I were curious if someone had any breakfast yesterday, I could ask:

Did you have breakfast? (Swedish: Åt du frukost?)

In the first example I'm referring to an interval of time that is ongoing - it's not too late to have your breakfast! In the second example the time interval has ended.

In English I think it's okay to say "Did you have breakfast yet?", but in Swedish that would never work ("Åt du frukost ännu?").

How would you express the distinction between an ongoing and an ended time interval in Esperanto?

And please, what are the correct grammatical terms so that I can update the question title?

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How would you express the distinction between an ongoing and an ended time interval in Esperanto?

It feels like your question is about the aspect of the verb.

Aspect is a grammatical category that expresses how an action, event, or state, denoted by a verb, extends over time.

In your example you could use yet/not yet if you want to know if it is too late to join the the other person's breakfast:

Ĉu vi jam matenmanĝis?
Ĉu vi ankoraŭ ne matenmanĝis?

But you could also use participles for that (see this question about ata/ita/ota).

Or use an affix to create a verb that as has a certain desired aspect, for example, if you find people at the table, but it looks like they already finished, in order to ask if it is too late for you to join them you could also say:

Ĉu vi fin(maten)manĝis?
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Verbs can be classified in several ways, one of them is the aspect. What the aspect denotes varies heavily from language to language. In Swedish as in other germanic languages (English being a Germanic-Romance hybrid has always its exceptions) different past tenses are used to shown what you described.

  • Har du ätit frukost? : the action is still going on or at least it did not end a long time ago
  • Åt du frukost? : the action has ended already some time ago

(Note, in the later case you almost automatically add a time-specifier, like Åt du frukost igår?, Did you eat breakfast yesterday?)

The aspect system in Esperanto is totally different. The main components are the prefix ek- and the postfix -ad, but those cannot be used to express the difference you mentioned. While there are the compound verb forms with their -anta/inta/onta endings in the active and -ata/ita/ota in the passive, thanks to the early Esperanto activist Kazimierz BEIN we commonly now use the simple verb forms with additional specifiers if necessary. In other words you do not need to mark the verbs but add other words into the sentence to communicate the meaning.

  • Ĉu vi jam matenmanĝis? : Har du redan ätit frukost?, Have you already had breakfast?
  • Ĉu vi ankoraŭ ne matenmanĝis? : Har du inte ännu ätit frukost?, Haven't you already had breakfast?
  • Ĉu vi matenmanĝis hieraŭ? : Åt du frukost igår?, Did you eat breakfast yesterday?
  • Ĉu vi ne matenmanĝis hieraŭ? : Åt du inte frukost igår?, Didn't you eat breakfast yesterday?

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