Modern Greek sounds much like Spanish to me. It is interesting, then, that having arisen, one from Latin and the other from Ancient Greek - quite different sounding languages - they somehow converged.

I wouldn't say converged.

Curious on the traits that sound similar to you.

To me they sound pretty different as a native Greek speaker. I can spot the loan words etc and can make some meanings, but that's where that stops. Spanish is pretty different from Latin too, in that it is simplified. Spanish has a really interesting history but a Latin speaker wouldn't be able to communicate with a Spanish native speaker in any way -- i.e. it has deviated substantially.

When I hear Spanish (from Spain) expecting Greek or vice versa, it does sound a bit like gibberish in the other language. Of course I speak both, so I quickly understand what's being spoken (at my current level, which is elementary in Greek).

Μένεις στην Ελλάδα?

Interesting. Usually both languages are too distinct to me/"my ear" to confuse them, but I do encounter that phenomenon with other pair of languages. Ans: I live abroad/SF Bay Area. Κοίτα προφίλ για επικοινωνία! Εσύ;

You probably have the better ear for it since your Greek is much stronger than mine!

Μένω στις Ηνωμένες Πολιτείες, αλλά θέλω να ζήσω κάποτε στην Ελλάδα.

I used the words ‘sound’ in its literal sense, i.e. I referred to phonetics.

Which was the interesting part for me! You are not the first person bringing this up. And it's peculiar, as my ear, at least, makes up some differences. But I am not sure how to describe or analyze these language phonetic deviations.

I think the similarity they're referring to is that in both languages, many plosives became fricatives, even though the letters remain the same.