Minecraft accounts and profiles

My daughters play Minecraft and up until now they have been sharing an account. (I don't play Minecraft and don't know much about it). Now, my younger daughter wants her own account. She claims that creating a new profile doesn't do anything and that she needs an entirely new account. And she claims that we don't need to pay to buy Minecraft again - that somehow our existing purchase can be shared across two accounts.

So, I created a new account for her, but when we log in it just says Play Demo. And it seems to indicate that we need to buy Minecraft again.

Can someone please explain to me two things:

1) Do you think that we need to buy Minecraft again to have a separate account? If not, how do I link our two accounts together?

2) Why isn't it good enough just to create a new profile under our existing account?

Added (1). the purpose of having a second account is not so that they can play at the same time (we only have 1 computer). The purpose is so that they can have different worlds, usernames and stuff.

1) yes you need to buy it again and no they can't be linked

2) you can't create a new profile on your account it is one profile per account. The plus for buying it again is if you have two computers is they can play together on a server.

For minecraft two people can't play at the same time on different computers (If they want to play at the same time you have to buy another account). Also you can't get another profile for free using the existing purchase - you have to buy minecraft again.

Also you can create another profile on the PC that has the account.
1: Launch minecraft (Just to the launcher, not the game)
2: In the bottom left it has your minecraft name click 'new profile'
3: at the top it has the profile name change it to what you want.
4: in the bottom left it has save profile click it and you have 2 different accounts on the one main account (Just click the name to change accounts)

I'm not sure that does anything after testing it, you may want to mess around with it also.

1. You have to pay for another premium account
2. Because a "profile" is just some data stored on your computer that determines some settings and which version of minecraft is launched by the launcher

The reason you can create multiple profiles on a computer is for easy switching between different launcher configurations.