Why I need to log in to www and non-www URL twice?

I can access my site on both www.mydomain.com and mydomain.com. But the problem is when I'm logged in to mydomain.com, I'm still logged out on www.mydomain.com, meaning I need to log in again in the later URL. I just don't understand why.

I've hosted my site on DigitalOcean droplet; I've created 'A' record pointing to the IP and CNAME record alias for WWW.

Can someone please advise where I've done wrong?

PS: what is the difference between, mydomain.com and mydomain.com/, both have https:// prefix.