Cartridge bottom bracket with lockring on one side only
Your standard cartridge and "loose bearing" bottom brackets have two threaded "cups".

Usually the right (drive) side cup has a lip on it, so it will only screw so far into the bottom bracket housing.  There is no adjustment, and no need for one, since the distance that the shaft should project outward is determined by the design of the parts.  And if the bottom bracket is a cartridge one often the right side cup is permanently attached to the cartridge.

However, nothing is perfect.  If the cups do not tightly restrain a cartridge unit it will move about and make annoying clicks.  And if the cups are loose in a loose bearing style unit the axle will wobble around in the bearings.

So one side (at least) is made adjustable, without the lip on the cup, but instead with the threads extending a few mm outward beyond the expected distance it should be screwed into the BB shell.  This adjustable cup is then screwed in "tight enough" to achieve the desired pressure on the bearings.  But "tight enough" is not generally so tight as to cause the cup to "lock" in place like a regular bolt, so the lock ring is added to allow the cup position to be preserved, in spite of the various mechanical pressures that would attempt to turn it.

Note that this "adjustable cup" is generally on the left side, allowing the adjustment to be accessed without interference from the chainrings.

The vast majority of "3-piece" BB setups, at least on lower-end bikes, are of this variety, with one "fixed cup" and one "adjustable cup".  For the most part these units are interchangeable, so long as the style of the axle end matches (and there are 3.5 different styles).  There will be a modest variation in the length of the right-side shaft, between 2-ring and 3-ring fronts, but most 3-ring bearing assemblies will fit 2-ring bikes, and likely a fair number the other way.

A few bottom bracket bearing assemblies have adjustable cups on both sides.  This allows for various things, such as a BB shell that is wider or narrower than normal, or desire to adjust the "chainline", moving the sprockets closer to the frame or farther away.  It also allows a single BB bearing assembly to fit several (slightly) different setups.