Can i avoid expensive fees buying and storing ethereum on ledger this way?

Hi everybody

I was wondering if when i buy ethereum through the option buy > buy crypto via Coinify on my ledger live, does this mean that once i buy it, it will store automatically on my wallet or it will be on the exchange and still need to move it paying those fees?

If it meant that it goes straight onto my wallet, i wouldnt be paying fees, am i right?

Newbie trying to learn, thank you!