Is being "sinless" the same as "being perfect"? Jesus taught us to be perfect He also taught us to be without sin.

Furthermore, He came to make us perfect and to take away our sin.

My question is: are these two states identical? If I were perfect, I would presumably be sinless. But if I were sinless, would that in and of itself be enough to be perfect? Or would I just be "not doing some things" but I would need to change other things in my life to meet my redemptive potential?
The word perfect rarely means sinless in the Bible, it generally means well rounded, or mature. The idea of a sinless Christian is foreign to the Bible, except of course those in heaven.

For example Paul uses the words translated into English as perfect here:


  12 Not that I have already obtained this or am already perfect, but I press on to make it my own, because Christ Jesus has made me his own. (ESV Philippians 3:12)


Here paul uses the Greek τελειόω teleioō ; to complete, i.e. (literally) accomplish. It means 'to fulfil', 'to carry out' a required course in the sense of a received commission.  As this rare context does actually imply actual sinlessness in that he aims for heaven, Paul, as our example avoids possible confusion saying he has in no way achieved it, but aims for it. 

In the case mentioned:


  You therefore must be perfect, as your heavenly Father is perfect. (ESV Matthew 5:48)


The Greek word for perfect is similar, it is τέλειος teleios.  Again it means something similar to complete, it means totality or undivided.  It does not mean sinless. From the context immediately before this verse we can understand the logic. God is unrestricted in His goodness, so according the disciples of should be 'total' in their love, even loving their enemies. The totality has to do with loving, not just some, but all.  This love would never have been presumed to be a sinless, pure love; just a total love in its well rounded and broad application without favouritism.