If you are a commercial photographer, then yes you would carry model releases with you, or use an app to record the information. Otherwise you would get the person's name and contact details and obtain permission later.

You have the right to take photos on public property, in public places where people don't have the expectation of privacy.

That doesn't give you the right to take those images and use them for commercial/advertising purposes without consent. By commercial I mean putting them on a billboard or website selling a product. You might be able to sell your prints as artwork, or enter them in competitions, if the rules of the competition didn't require waivers, which most seem to do these days.

There is a country-specific table of rights, including commercial here

A good reference on the subject here, which includes

Typically, before you can use a picture of someone in an advertising campaign or for other commercial purposes, you need to have the right to copy the photograph (a copyright license from the photographer) and the right to use the individual’s image (typically achieved with a “Model Release” from the individual).