There are three main types of bike tyre - tubular, clincher, and tubeless.

Tubular tyres are the older design, in which the tyre and inner tube are one singular unit, and this is the type that needs glued to the wheel - you probably don't have this unless you bought an older racing bike or wheelset, but it's worth mentioning so you know the difference. Some people still swear by them.

Tubeless are pretty self explanatory, they're basically clinchers without an inner tube, and it sounds like you know what they are so we can move on.

Clinchers are by far the most common, and consist of a tyre over a separate inner tube - the pressure of pumping up the inner tube presses the inside of the tyre onto the inside of the rim, hence 'clincher'. If that's what you mean by 'standard' tyres, then no, no glue is needed.

Assuming you have clinchers, there is a knack to fitting them if you've never done it, so I suggest watching a quick video on it if you're unsure, just to save you a bit of head scratching.