From my perspective being a Catholic Convert from a Pentecostal church background.
As a Protestant, looking back I found it difficult to see Jesus as both God and Man. Though I knew that was true. The Scripture that stated that Jesus laid aside His deity and became man, I think some Protestant believers have a difficult time calling Mary the Mother of God. That’s the difference.
The difference is: In protestant churches people stop short of calling Mary the Mother of God. She’s the mother of Jesus but somehow not the Mother of God. But we know Mary if the Mother of God because Jesus was always fully God and fully Man.
I think, as is in most cases it’s rather a difficult doctrine to explain. However, if a Protestant believer has any theological understanding at all they’d understand that they believe in the same Jesus as Catholic’s do. I think at times though they stop short of calling Mary the Mother of God because then that would mean lifting up Mary to be the Queen Mother. But as is always the case, Mary has always been the dividing point among Protestants and Catholic’s. If anything, my changed understanding of who Mary is has caused me to reverence Jesus even more to understand that Jesus was always divine within his humanity.
So in short … not a different Jesus. The difference is with certain Catholic teachings, Papal Authority, Sacraments of the Catholic Church ie Confession, calling Priests Father, who Mary is, praying to the Saints and Mary… these doctrinal differences is what separates us in our faith but we worship the same God and we believe in the same Jesus.