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?
I don't think if the wallet you are holding your bitcoin matters here. What is the main thing is your stacking and holding for a very long time.
I read somewhere in at my research about crypto that "hodl" was a mistaken written word by an investor who meant to say "hold". Then it became popular and was adopted for crypto language.
So it literally did not State about wallet differences but about investors who either buys on Dca or just once but must hold (hodl) for a longer time nomatter the market fluctuations.