There are many types
I have removed, or been involved in removing, several hundred wild honey bee colonies out of places they have chosen for their own home and built their own nest. The spacing in combs of any reasonable size is usually 36-38mm between centres, although this may vary slightly where there are small pieces of infill comb.
In a wild nest, combs are used for rearing brood and storing food in, unlike a managed hive where we have brood and food separated. The length of brood cells is usually consistent for obvious reasons, but the length of a food cell can vary considerably. For this reason brood frames in a managed colony are spaced close to what they would be naturally, yet super combs can be spaced wider. This has given rise to what in the U.K. and Ireland is known as "narrow" or "wide" spacing, although frames of foundation should only be put on narrow spacing until they are fully drawn out, otherwise comb is likely to be built between the foundation. When drawn. the combs can be put on wide spacing.
In the U.K. narrow spacing in "metricated imperial" is 38mm and wide 46.5mm. To the best of my knowledge it is only the U.K and Ireland that has "wide" spacing as a standard. I suspect the reason for this is because in the U.K. frames have "long lugs" (38mm), where the rest of the world have "short lugs" (length varies between 17-19mm). This allows most types of spacer to be used on long lugs, including those such as metal/plastic ends that slide over the lugs. This isn't easy with short lugs because the spacers easily fall off the lugs, so self spacing frames where the side bars are wider, such as "Hoffman" are used.
As most of the world uses short lugs, it is difficult to space frames by any other means than the self spacing Hoffman side bars (termed "end bars" in the U.S.). The width of these varies confusingly! As far as I can find out Langstroth are 35mm wide, yet Dadant are 38mm wide, which is the same as the U.K narrow! To make it even more confusing U.K. Hoffmans are 35mm! But why? I have found absolutely no reason for this.
As Hoffman frames are only made in "narrow" size, you will need another spacing method if you want wider spacing in supers, for when the combs are drawn out. Many beekeepers don't bother, but for those who do, there are two methods usually employed. These are "Stroller Spacers", that are a similar principle to castellated spacers and are nailed on the inside of the super, or what is termed a "Frame Spacing Tool". The latter is simply a flat piece of metal or plastic with angled slots in a bit like a comb, so the frames can be located in the slots and removed, leaving the frames loose in the box, but spaced correctly. Before I saw the commercial one I tried this, but found that the slightest knock moved the frames in the box, but I was using narrow frames, not Hoffman that still have spacing, albeit narrow.
The standard frames (DN/1 and SN/1) in the U.K. and Ireland are 22mm wide all round, including the side bars. There are two relatively common types of spacers that fit over these, Yorkshire spacers and Hoffman converter clips. The latter allows compatibility with standard Hoffman frames.
For long lugged British frames castellated spacers are popular in supers, but for some reason are not popular in brood boxes. I think that's a pity, because I have used them for over 40 years and find them much better than other forms of spacing. I suspect it has more to do with people having never used them than anything else, but that attitude is a major problem throughout beekeeping.
Manley frames are quite popular in the U.K. and Ireland, with occasional use elsewhere. The side bars are parallel self spacing with widths varying slightly (41-43mm). They are used for supers only and are part way between narrow and wide, allowing 10 frames in a B.S. National box.
Over the years a number of items have been used including screw eyes, hob nails and ball headed corkboard pins, but although they have suited some beekeepers, there are enough suitable methods that I haven't included them here. They may, however, have their uses for odd sized frames.
A link is provided for Beesy frames, as they have a somewhat different spacing method. Abbott frames have been retained because of their historical significance.