During my doctrinal oral exam one of the questions we could anticipate was related to salvation.  We were told the question could take the form of something like this:  "In what aspect are you saved?"  And in our preparation I remember one person saying that a good answer would be this:  "I am saved.  I am being saved.  And I will be saved."  Romans 8:28-30 supports this view.
If the words 'saved' and  'converted' are synonymous, and I believe they are, then the narrative in Acts 10 gives us an account of one person being saved (converted) in the past tense of the word.  And one person being saved (converted) in the present tense of the word.
Cornelius is a religious God-fearer who is being relentlessly and mercifully pursued by God.  The coming of the Holy Spirit on him (Acts 10:44 ff) and his subsequent baptism confirm his conversion at a point in time.
Peter on the other hand is the example of one who is being saved, being converted.  Think of the revolutionary change in his perspective that took place as a result of his vision in Acts 10:9-16.  And then his amazing statement to Cornelius in vs. 28: "...God has shown me that I should not call any man impure or unclean..." (NIV) That is the progressive nature of conversion as God continues to work on our hearts to expand them to love as he loves.  There are other ways this expansion takes place.  But the crucial one is in our love for those who we at one time or another considered un-loveable.