I don't think you can really distinguish between the two unless the person tells you that it's spelled a certain way.

There isn't really a way to distinguish them while speaking, if it's written i mean it's easy, but they are just different spellings of the same day

"Monica" (sometimes with an accent mark on the "o") is the usual spelling in Latin languages such as Italian (but in French, they often use "Monique"), while you would mostly see "Monika" in German, Polish, or transliterations from other alphabets (such as Cyrillic). I get the feeling that "Monica" is the usual spelling in English, but you'd have to check online (you can check on the US government website, which has the most common baby names by census year, or something like that).

Hello Monika, I feel both are same.