Forgot Apple ID password for my iPhone

I forgot my apple id password for my iphone; and so i simply created another id, with a new password.

Trouble is, when i try to GET/PURCHASE a new app, the PREVIOUS apple id appears, and i am asked for the Old/Previous password.

How do i change this to make the NEW apple id appear.

Also, i was sent a Link from a Business recently and when i try to access it, the OLD apple id also appears on my phone asking to enter the old, Lost password.......do i have to get the Business to send the Link again?

[Re-Titled by Moderator]