It varies widely from place to place I find. For example when at WWT I could tell from a glance a male from a female goose/swan/flamingo etc by whether the ring was on the left or right leg.
Place I'm at now it doesn't matter what leg as long as it's the correct size for the species and on properly, and the colour is what we get out of the bag until we run out of red or gold ones lol
As well as an identifying number or letter for that individual bird, rings sometimes have the initials of the collection they belong to; such as NBPC for the (then) National Bird of Prey Centre, or they may have a telephone number to call if you find the bird (BTO sometimes do this, Her Majesties Estates, and more often racing pigeon types), or if the bird is from a private collection it may have the initials of the owner or bird ringer. Rings from Europe often have long sequences of numbers and letters, while a lot of UK collections have short letters or/and numbers.
Sometimes a coloured plastic 'wrap' is put on a bird to distinguish it from others easily on sight without having to catch it up, but these are meant for short term use compared to the metal rings. Metal rings come in 'closed' (solid) and 'open' too. Closed rings are put on young birds, when their bones haven't become fully solid and slip over the still flexible toes. Once the bird is fully grown the closed ring is permanent (unless cut off of course). A closed ring is a sign of a bird rung as a juvenile or in the nest. Open rings are more common as they are easier to apply and can be put on any adult bird that comes into a collection. By 'open' they are a 'C' shape that is closed using a specialised tool around the leg until the ends meet neatly and smoothly. Open rings could be 'open' to fraudulent use; potentially on birds illegally taken from the wild. On the plus side for open rings they are a lot less invasive to a nest and less likely to cause accidental injury to the bird while being fitted. Horses for courses in some ways.
When birds are moved around from collection to collection and country to country you will get a range and mix of rings on show.
As long as the paperwork or computer records match that individual bird with that particular ring it doesn't really matter that much in a way. With some species, European for example, it is becoming a requirement to have them microchipped rather than ringed. At the moment this technology is rather invasive for smaller species but as with everything, inevitably this will get smaller and easier to use. Ringing has an advantage over microchip as you can see it without needing to get close enough to use a microchip scanner.
That just about covers everything I can think of right now, there may be more I think of later. Hope this helps.
