Who exactly should be referred to as a
HODLER? As we already know, hodlers are people who hodl bitcoin for long periods of time; they are determined not to sell for the long term irrespective of the price change.
Now here comes my question: If those who buy and hodl their coins on a noncustodial wallet where they have full control over the coin are referred to as hodlers, are those who also hodl under a custodial service where they don’t have full control of the coins also regarded as hodlers?
If you leave your coins on a custodial exchange, the exchange is the one holding your coins and not you. What's available in your balance is what they can manually input. Since you don't have full control of the coin, you shouldn't be considered a hodler.
When you invest your money in Bitcoin or any other coin and keep it for long-term holding, be it in a custodial exchange or a custodial wallet, then you are definitely considered a holder. Because even if you keep your coins in a centralized exchange, even though you do not have full control over it, you are still considered a holder because you own the coin. How you keep your assets and how secure you keep them is entirely up to you, so it does not matter where you keep your coins. I think you are considered a holder no matter where you hold them.