They are two different past tenses that are -I think- unique to Turkish.
-miş indicates uncertainty, like you have heard of something, it happened while you weren't there.
-di is more certain. You are sure it happened, you have seen it with your own eyes or it is a really common fact.
the past tense part here is "-miş", which is the "narrative past tense". This indicates that the speaker didn't personally witness the action, or that there is uncertainty about what happened.
The verb root here is "özle" (infinitive: "özlemek").
Present tense would be: "Anlaşılan sen beni özliyorsun". The present tense suffix "-iyor" causes the final "e" in the verb root to disappear.
Hey Mark! :) thanks for your elaborated explanation! I was asking, though, how would you say it in present tense with a narrative. Or in other words, what's the difference between past and present tense when it comes to the narrative?
Or is the narrative suffix used only in the past? I'm confused. How do you indicate that you do not witness or only hearing through someone else, but in the present.
Ah. Yes, in Turkish, the narrative tense only exists in the past. There's no way to use "-miş", for present tense, and no equivalent to use either.
Other languages have more robust "evidence" markers, for indicating how you know the information you're presenting. So the concept you're thinking of obviously exists. But in Turkish you just have to use context or specifically say that info.
The Past Perfect Indefinite is formed by adding the indefinite past tense suffix ‑miş to the past tense ‑miş form of the verb.
There is hearsay or doubt in the meaning of this tense as it is made indefinite and unspecific by the addition of the past indefinite suffix in ‑miş.
This tense signifies the indefinite Past in The Past. "(I thought) I had done it."