There are stones and runes. The first time I encountered a rune, it was a production rune. There are very few of these, "link rune", "disenchant rune", "blend rune", "purify rune", "frost rune". They are used for crafting. For example, my tailoring uses a single disenchant rune for each item higher than level 10. Disenchant runes drop from butterflies. Most production runes are sold on the auction house for an average of 500 gold. If they are more expensive, you can buy cheap items from a vendor and use your disenchant skill to turn them into production runes, sell the ones you don't want and keep the ones you need.
The next rune I encountered was the stat rune. These behave similar to regular stats, except that they go into a rune slot on your item. Usually stat runes have a single stat with a particular level, although there are ones that have special abilities, or two stats. An example rune is "Resistance I" which increases your stamina (or defense, I'm not entirely sure). You can combine five of these runes into a rune of a higher level (for "Resistance I" that would be "Resistance II"), using the arcane transmutor. You can also combine two runes into a two stat rune, although there are special rules for this and some of these don't work, and the resulting stats might not be what you expect. There are two stat runes that drop from the Ancient Treasures mini-game. In my opinion the best place to get the single stat runes are the events around Dalanis, as they give rune bags that sometimes contain V runes. I don't recommend combining runes less than IV, as it is a waste of charges. Sometimes the item shop sells very high level runes for a reasonable amount of diamonds. As I said earlier, some of these have special abilities, like increasing the speed at which you can cast a spell or (for Reconciliation runes) how angry you make monsters (your so-called aggro). Runes can have different effects based on which item you add them to, and some runes only work if they are in a weapon.
The events around Dalanis also provide fusion stones, which are used to turn items into stats. These can also be bought from spirit mages, who sell them in most major cities, the "Stamina I and two random attribute" is preferred, unless you're using them for tiering, in which case the "Random Fusion Stone" is sufficient. There are also fusion stones you can get with honor, or from the Naga event. All these fusion stones are considered "dirty" as they have green stats on them, which you usually don't want, as they will transfer to your new item. Clean fusion stones ("purified") can only be gotten from a bag quest in Ystra, or from the item shop. A fusion stone is combined with an item to create a mana stone, which will be covered in the next paragraph. The ancient memento vendors also sell fusion stones with very high green stats on them. With a lot of creativity you can use these as clean fusion stones, provided that you use slightly lower yellow stats (e.g. the Yellow VIII stats with the latest fusion stones). I doubt the cost in ancient mementos is worth it, and you might still need to use at least three purified fusion stones in order to kick the green stats off your item, or prevent them from appearing.
Mana stones are created by merging a fusion stone with an item, and can have up to 6 stats on them, just like a regular item. Mana stones have a tier, and only mana stones with the same tier can be used together. Mana stones are always used in groups of three. You can either combine them into a mana stone of a higher tier, or apply them to an item, which will get the tier of the mana stones and receive all the stats, although in combining the stats it always takes the lower ones (green stats are generally considered lower than yellow, but the numbers are relevant too). Mana stones are for sale on the auction house and can be bought from other players, but I don't think there are any other purchase sources.
I recommend keeping the naming of these separate. You're free to call a mana stone a "tiering stone", especially if they contain 6 green stats or are higher than tier 5. But don't call fusion stones or mana stones runes, or the other way around.