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.
Not your keys, not your coins (and not being a HODLer)
Your keys, your coins (and you are HODLer)
You already answered the question in the first sentence when you define the word hodlers.
It didn't say what wallet needs to be used to be considered as a Hodler or where they need to hold their coin.
Hodlers are those people who bought and hold their coin for a long period of time.
Now if those who owns Bitcoin for a long period of time and had it sitting in trading sites and didn't sell it aren't consider as HODLers then what should we call them?