I understood (from what I've read - and rightly or wrongly) that the words for peace and submission are cognates, but that the primary meaning is submission.
One of my sources from Dr. Mark Durie's web-site:
"Words for ‘peace’ in European languages imply the absence of war, and freedom from disturbance. It is no coincidence that the German words Friede ‘peace’ and frei ‘free’ sound similar, because they come from the same root.
While there is a link in Arabic between salam, a word often translated ‘peace’, and Islam, the real connection is found in the idea of safety.
The word Islam is based upon a military metaphor. Derived from aslama ‘surrender’ its primary meaning is to make oneself safe (salama) through surrender. In its original meaning, a muslim was someone who surrendered in warfare.
Thus Islam did not stand for the absence of war, but for one of its intended outcomes: surrender leading to the ‘safety’ of captivity. It was Muhammad himself who said to his non-Muslim neighbors aslim taslam ‘surrender (i.e. convert to Islam) and you will be safe’."
He cites Lane's Arabic-English Lexicon on the root s-l-m. The full link is here:
http://blog.markdurie.com/2015/12/anyone-using-phrase-islam-is-religion.html