Arent ancient and modern Greek pretty different though?

Yeah, after about 1000 years even the exact same language normally will change so much that it's not understandable to speakers on opposing sides of that divide. I can't read much German, but in reality German and English are very related and with some explanation one can see it pretty clearly. I agree with your sentiment I think, but "nothing like" is pretty absolute.

have absolutely nothing in common.

They are both Indo-European languages and it shows. The words for father and mother for example, are very similar in the two languages.

I will never understand why people always want to deny the interconnected nature of the universe and instead want everything to be unrelated and separate

I mean they are fairly similar. They share a lot of vocabulary, their nouns have corresponding declensions, verb conjucations are similar, there are a lot of other similar grammar constructions, and the Latin alphabet is mostly derived from the Greek alphabet, too.

Edit: Classical Greek and Classical Latin, at least. Modern Greek and Romance languages like Italian are further diverged from those ancestor languages to the point that they are difficult for modern speakers to even parse.

It's still all Greek to me

Ars longa, Vista brevis.

No they are not. They are both Indo-European but each is from a completely different branch of the Indo-European languages. Latin stems from the Romance branch, while Greek from the Hellenic branch. Other than their common "ancestor" language group, the only other similarity I can think of/find right now is that Latin did borrow many Greek words due to the Roman's heavy influence from Hellenic culture. However, this doesn't mean that they are at all related.

Greek itself has myriads of Turkish words due to the Ottoman occupation of the Greek lands (Greece as a nation state did not exist yet at this point if I'm not mistaken) from 1453 until 1821(almost 400 years), however it would be ridiculous to make the claim that Greek and Turkish are related, given that Turkish is an Anatolian language which only shares commonality with Greek due to the fact that they are both Indo-European branch families. Hence, it is ridiculous to make the claim that Latin is related to Greek simply because they borrowed many words.

So, linguistically speaking both Greek and Latin are from majorly different language families, and we have discussed how you can't make the claim two languages are related simply because they borrow words from each other because of various political/historical reasons.

You are confidently incorrect.

https://glosaidiomas.com/greek-vs-latin-origins-and-differences/

https://autolingual.com/greek-vs-latin/

In thoroughly confused. They're not even similar.

They are in fact, not, but I always confuse them