Greek looks very different from Latin because of their writing systems (e.g. the Greek alphabet has some different letters which, like Cyrillic, make it look very exotic to us). But to someone who knows both Latin and Greek it is clear that the languages are related. How the nouns are declined, how the verbs are conjugated, irregularities in both languages that are unlikely to be accidental and so forth.
Suppose one language uses an internal vowel to determine tense: --i-, --a-, and --u-. Swim, swam, swum. Sing, sang, sung. Now suppose you came across a language that had the verb "ring" as in "to ring the bell" and it was conjugated ring, rang, rung. You might suspect the two languages were related. But if there were hundreds and hundreds of those similarities, far more intrinsic to a language than mere borrowed words, then you would really have to wonder if the languages were related in some more fundamental fashion.
"The Sanskrit language, whatever be its antiquity, is of a wonderful structure; more perfect than the Greek, more copious than the Latin, and more exquisitely refined than either, yet bearing to both of them a stronger affinity, both in the roots of verbs and the forms of grammar, than could possibly have been produced by accident; so strong indeed, that no philologer could examine them all three, without believing them to have sprung from some common source, which, perhaps, no longer exists."You may wonder what that may have to do with you, or with anything else in the modern world. The answer is, everything. But that will be for another time.