Recently I noticed that some casinos offer an option they call 'play for fun' and 'real play', which are also the same things as 'demo mode' and 'real funded account play mode'.
Now my question for the casinos which label demo mode playing as 'fun' is, does it mean that those who place bets with real money are not having fun and are just after chasing for a chance to increase their staked money, or what?
Demo is meant to learn how the game works while giving you that gambling experience and entertainment, but referring to it as 'fun play alone' makes real bettors, to me, fall under the category of desperate gamblers.

As you said, the demo game is only for learning and playing experience, after real money is played, that's where the fun comes in, in my opinion, because the bets made involve real money so you are more serious and focused on playing, unlike the demo mode where you make random bets.