P&S stamps can also be, and usually are, soaked off the paper too, but it's much harder and takes longer than with sheet stamps, and you are more likely to damage them by tearing or by "thinning" parts of the rear paper texture of the stamp. Some issues are worse than others, depending upon the combo of the stamp paper and the degree of impermeability of the adhesive layer.

Some US (and other) collectors do leave them on the paper, which is not surprising to anyone who's tried to soak US stamps off paper, they are mongrels to try and get off. The same with some other countries, they're all different.

Mint P&S stamps are collected and left on their backing papers.

Stamp hinges are still used, but only on used stamps.

The standard for post-1970 stamps is "MNH", ie Mint Never Hinged, and even for 1950-1970 stamps lightly hinged stamps sell for less than MNH.

Nowadays they are stored and displayed in hingeless albums, or stockbooks, where you slide them into clear non-adhesive strips or pockets attached to the page. You can see these display sheets on almost any scan on the Stamps listings.

Now you know the lot Dave, time to get out your childhood collection and rejoin the world's 60 million philatelists.