>Oh right. I'm entitled to a lawyer if I'm ever taken in for questioning. I didn't realise it was so different.
>Can the police just question you and you have no right to legal representation?
No. You always have the right to legal representation -- at your own expense and, in criminal cases, depending on your financial situation, a court-appointed attorney. In many places, the state will only provide an attorney if you're indigent -- and can prove it.
The Miranda Warning[0] (not Miranda "Rights") is generally required if you're being arrested and/or detained for "questioning."
However. the rights mentioned in those warnings (right to remain silent, right to an attorney, etc.) don't magically appear when the warnings are given. They apply regardless of whether or not the warnings are given -- whether you're a suspect, a witness or the object of a police officer's lustful desires, etc.
What's more, the police are legally allowed to lie to you (e.g., "we have your fingerprints on the murder weapon." to get you to waive your rights).
As I understand the primary change over the past 20 years or so is that if you don't positively, verbally/in writing unequivocally invoke your rights to remain silent and have an attorney present, the police may ignore less unequivocal assertions.
>That's the bit that sounds odd. Surely they can't just claim you're not a suspect yet and therefore deny you a lawyer?
IIUC, In a non-custodial situation, they are not required to provide the Miranda Warning[0]. However, the rights mentioned in that warning exist and are in force regardless of your status (custodial/non-custodial). One may invoke them at any time. I recommend doing so loudly if you're within two or three meters of law enforcement.