Wouldn't it be more correct to say that Muslims spread through conventional warefare and Islam spread through proselytization and incentivising conversion? I w

Wouldn't it be more correct to say that Muslims spread through conventional warefare and Islam spread through proselytization and incentivising conversion? I would imagine Muslim empires could expand without conversion (as they most definitely did in some areas) and Islam spread without a political presence. Like, I always thought that the Umayyad elites sometimes didn't even want people to convert, lest their privilege become diluted.