The use of runes and bezels are to generally make a character stronger, more durable, less fragile, or more effective by being applied on items. They can be used together on an item as long as there is a rune and a bezel for that item.
About the rune and bezel types and their differences:
Mainly there is one big difference between bezels and runes:
Bezels give an item a characteristic the item didn't have before while the runes boost already existing characteristics. Of course, there are some exceptions. Other than that, there's also the option of runes being upgraded with special items called Elements which increase the stats of the runes and/or add new stats to it. That, however, is not possible for bezels.
For example:
Protection Bezel B'yal I and its variants as well as most of the other bezels found in the Arsenal in Hell's Pass/Foothills give the item a new characteristic called Durability which makes the bearer of the item to receive less direct damage, but a
Rune of Hurricane Fav boosts the item's already existing characteristics of Agility and Strength, which indirectly helps the owner receive less damage (by dodging more) and directly helps him/her deal more damage by giving the item more strength.
However these are two small examples. Other than these there is
Bezel of Negation and its variants which help the owner of the item receive lower level injuries when they die. There are bezels which:
1- Increase initiative
2- Increase trauma attribute
3- Increase penetration of magic
4- Increase protection against magic
5- Increase succesful gathering chances
6- Increase maximum fury reserve
7- Increase the chances of trippling procurement and reduce unsuccesful gathering
And finally, 8th one, the type of bezel which affects one's fighting, making them more durable to stuns, make them stun more frequently and boost their advantage in battle.
These were the bezels, for runes, there are mainly 4 types of them: Runes which can be made, runes which can be bought, runes that are given by the game
and runes which can be received by participating in events.
1- Runes that are made by players are the ones that increase stats of an item, they and their elements can be made by Jewellers. (Please note that only blue runes have elements, green ones don't, however this doesn't apply to Sid Speed Rune as it's a special kind of rune which has all variants from gray up to purple).
2- Runes that are bought from various shops in the game are types of runes thata don't belong to first group of runes. These ones can also be upgraded with elements, yet they are not bought from players, instead from Arsenal or Trade Fair. Two examples to this group are Sid Speed Rune and Bow Runes.
3- The runes that are given to players by the game. These ones are simple gray runes that give small stats to items with the purpose of teaching newcomers how the game mechanics work.
4th and the final type of runes are the runes which can not be bought in game shops with gold, can not be made, nor are given by the game. These ones are bought in game event shops with their specific tokens. An example to this one is the tool rune (the rune is received according to your first/gathering profession) received from Runic Casket which is a reward that can be bought in the event shop of May Mess event.