Roses

I am going to again attempt to grow a rose from a stem from my beautifully scented yellow rose, I half succeeded last year, tried with 1 stem in a potato, but I tugged too hard to see if it had rooted and damaged the new roots, (too impatient) which surprisingly had grown. My query is, if I'm successful this year, and not kill the new roots, will it become a true rose bush?  I am confused as I have read that most roses are grafted onto a different rose. What is the purpose of grafting roses?  In a comment o a previous thread someone mentioned that most roses come from Africa? and are grafted from the same white roses, even though the attached rose, in question, is supposed to be pink, but the suckers from the graft were white, therefore there were more white roses than the original pink.  All a bit confusing.