Walaikum Asalam,

Thank you for your thoughtful question. It can be a bit of a sticky question depending on whom you talk to. People prefer one term or another and sometimes get offended if you use the wrong term. And the source of this difference in terminology depends on what each person believes fitra, or our innate human nature, means.  

Those who call themselves “reverts” do so because it was revealed to the Prophet (PBUH) that each of us is born believing in Allah Almighty, as a natural belief, and that we instinctively know right from wrong. Therefore, Islam is the natural religion of each human being. And if we are left to our own devices, and not made to follow other religions by our families, each of us would stay on that natural religion. So, accepting Islam after having been raised in another religion is just a coming back to that nature–a reversion back to our fitra. This is from where the term “revert” comes. 

While those who prefer the term “convert” agree that the fitra is truly our nature, they also believe that to be a Muslim requires knowledge and choice; and we are not born with knowledge and as children, we don’t have a lot of choice in the religion we are raised. To find out more about why some people choose to stick with the term “convert”, check out the link here: http://aboutislam.net/reading-islam/living-islam/convert-revert-matter/ where I have explained my personal choice to refer to myself as a convert.

I hope this helps your understanding of the issue of terminology. All the best!