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Tier just determines how high it can be above. I believe they're still a range but I'm not certain.
When you start, any gear you get often drops at a slightly higher power level than what you have, based on the highest power that character can achieve. Note that this is not your currently equipped power, but the power of the highest level equipment in your inventory, and I think even bank (possibly weapons on other characters can count too, less sure about that, but other class armors don't).
This trend continues until you reach the soft cap, which is 900 assuming it didn't change for this season. Regular gear drops do not naturally drop higher than 900. The only way of getting higher gear from this point is "Powerful" drops. From this point on, regular drops will be the same or slightly lower than your highest power level, so they can still be used for infusing old equipment up to level and such. Powerful drops mainly come from "challenges", those yellow icons on your map with a powerful engram listed as the reward for doing things like playing a few crucible matches, completing 8 gunsmith bounties, and so on. Prime engrams, which are random drops from enemies, are also powerful.
Powerful gear will drop at higher power until you reach the Powerful cap, which is currently 960. After that, like with normal gear, powerful drops will not increase your gear level, only Pinnacle sources can. Like with powerful engrams, pinnacle engrams are listed as rewards for certain end-game activities, such as doing a high level nightfall, or the most recent dungeon and raid.
Stats are a bit harder to tell due to the randomness, but only certain activities have noticably higher stat drops on armor, primarily Iron Banner and raids from what I know.