Saving money is entirely different than saving bitcoins. In saving money, you are not gaining anything and your money will still be worth the same when you first kept it. Whereas in saving bitcoins, you are getting some profits off of what you're keeping that it will somewhat tempt you to take it out when it received some form of appreciation. That's the main difference, and that's what makes saving bitcoins harder than saving money - there is always the possibility of realizing profits in a short span of time.
I don't look at the outcome but the process. The outcome, as you said, is different, but the process is very similar.
When someone is good at saving money he should also be good at saving bitcoin because this attitude is a habit and a part of our personality. I'm good at saving, I'm a saver not a spender and this manifests in being a good holder. I also save up fiat money, I used to do that a lot when I was at school but now I spend more fiat and try to save up as much bitcoin as I can.
I know a few spenders and they just can't keep money at hand. If you hide it from them they will live like normal people, but give them some cash and it's gone.