Why does a PDF have two different passwords?
The format defines a user password, which is needed to open the document at all, and an owner password, which leaves the document readable but marks printing, copying, editing or form filling as not allowed. A file can carry either, both, or neither.
They behave very differently. The user password is real encryption: without it, the content is unreadable ciphertext. The owner password is a set of flags inside an otherwise readable file, and readers are simply asked to respect them.
Is removing the password legal?
Removing protection from a document you own, or that was sent to you with the password so you could read it, is ordinary file management — the same as saving a copy. Bank statements, payslips and insurance documents arrive encrypted with a password you already know, and retyping it every time is the only thing being removed here.
Cracking a password you were never given is a different matter, and no tool on this site does it: you have to know the password for the file to open.
What does the unlocked file look like afterwards?
The pages, text, images, links and bookmarks are identical, because decryption does not re-render anything. The file size usually changes a little, since encrypted streams compress differently from plain ones.
If you need it protected again with a different password later — a new one to share, or stronger encryption — add it back and choose AES-256.