You are also partially correct about the point of subduing - but that is only in one part of the Koran. Another part says "Kill the infidel if they do not submit to Allah". The Koran is a highly contradictory book.
Dhimmi status is somewhat related to what you compared it to with the exception that the aim was for Dhimmis to convert. In fact the prophet mandated at the end of his days that Arabia was to be cleared of infidels.
I agree the Koran says to kill the infidel IF he doesn’t submit. Those who submit are (supposed) to be treated as I said. In practice this treatment has varied from near equality with Muslims to pre-Holocaust Nazi treatment of Jews (ghettos, special clothing, limitations on occupations, etc.)