Interestingly while a pen scribble on either of those things will serve to render them invalid, the same is not true for bank notes, which will be happily accepted with all manner of markings upon them!
Well, banknotes are intended to be reusable multiple times, and in many countries indefinitely, while train tickets and stamps are intended to be used once, so they're not really comparable.
Scribbling on season tickets or rovers (as long as it's not in any date boxes) doesn't invalidate them, although once a guard decided to date clip my 3 day rover when I was travelling at 4pm on the final day. This just happened to be my final trip although he didn't know that.
When challenged, he said he did it "just to say it's been seen", but if that had happened every ticket check, he wouldn't have been able to read the ticket by then!
Most of the writing on banknotes comes from bank tellers writing the total on a big pile, or occasionally you find banknotes with love letters in the possessions of people who have passed away.
Once I found a banknote signed by the Beatles, which I bought for face value and sold for 20x face. The owner was a foreigner who was trying to exchange it in the UK but was refused as high street banks no longer do it for people without accounts, so asked me to bank them, and it was only by luck that I noticed.