One of the interesting things I've heard about morse code is that once you get familiar with it you can start identifying who is sending by the slight variations and syncopations in how they send. It is almost like everyone has their own voice that is often identifiable to those familiar with it.
That is true, but it's mostly true of people sending using a straight key (basically a simple button) or a bug (semi-automated key). Most morse code operators these days use a keyer paddle, and a fair number use a computer to send morse code. Since those generate the actual dots and dashes for you, and have precise timing, you end up with less variation between people.