Can anyone confirm if salama is at all related to Shalom/salaam?
Yes, it's a loanword. Swahili has a lot of words that derive from Arabic.
peaceful = ya maani, salama = safe
Today is peaceful = Leo ni siku ya amani
So what "Leo ni salama" means?
What is the difference?
Yes. Today is peaceful may also indirectly translated as Leo ni salama literally today is safe.
Peace brings safety