Difference between Bitcoin and real money is really big. Bitcoin is digital currency which means it's don't have any physical attraction. While real money, you have it in your hands, you have the presence. Bitcoin is just a virtual currency over the internet.
While other cryptos and alts have developed blockchains where the main use isn't as a form of a digital payment system... I believe that bitcoin was originally designed to be used as a form of a monetary instrument. It was definitely supposed to be like money. From the words of Satoshi Nakamoto himself:
[Bitcoin is] A purely peer-to-peer version of electronic cash would allow online payments to be sent directly from one party to another without going through a financial institution.
So he even states that bitcoin is supposed to be a form of internet money. But just because he
says it's money, doesn't make it money, per se. For example, if someone handed you $100 in PayPal, is that money or is that simply company credit? Are PayPal funds money? Or are PayPal funds the same as getting in-store credit from Amazon or Walmart?
How different is bitcoin from in-store credit and PayPal funds? And to get this answer, you have to think about bitcoin's usability.
1. Bitcoin isn't controlled by any one corporation.
2. Bitcoin has value because it can be traded for a certain value of fiat.
3. Bitcoin can be used anywhere to exchange it for goods and services, like fiat. PayPal and Walmart credit can only be used via PayPal or Wal-mart – and these credits are tied to your personal account. Bitcoin is not tied to any personal account – you can send a bitcoin to someone's address, and it's logged as theirs, just like sending funds from one bank account to another. You can't really do the same with Walmart credit because the credit is tied to your account.
Money, fiat, shares these same 3 properties with bitcoin. The only better difference between bitcoin and money is that bitcoin isn't owned by any government or corporation. It's literally an open-source global currency that's neutral to politics. If I could compare it, it would be like gold or other valuable metals – except that it can be sent and received within seconds between huge countries (unlike gold and silver).
So I agree with you that bitcoin is money, without the physical aspect.