How Email works..

Hi! I had a doubt in Internal working of an Email service. Hope i can get my answer here!

So I got to know the story till this,

We need MUA (or Email client) to send an email, MDA then takes it and delivers if the Email is in Local area network. But if its on the internet, then it is picked up by MTA. I am fine till here. I wanted to know what part SMTP plays in all this. Is it that when we hit send, the email is directly sent to SMPT server and then from there using DNS servers, an appropriate MTA is selected and the chain continues? Can someone please explain in detail about this?