Okay just to make something clear: While Muslim rule spread by force, getting told “comvert or die” was generally a very rare occurrence. Better living conditions for non-Muslims were a thing depending on the time and place, but even then the Islamization of the modern Muslim world outside Arabia was a very gradual process that took, for example, four hundred years in Egypt of one-sided cultural osmosis. Admittedly there was some foul play involved at some points, but almost nobody was converted at the tip of a sword.
Convert, pay up an extortionate tax and/or become a slave, or die, is forced conversion.