A crypto hodler should be someone who has the vision of long term hodling. It is unimagining that some hodlers prefer an exchange to hodl their crypto assets for them, denying them the right to have full access to their crypto is coins. Despite that, someone who has their crypto assets on an exchange or their crypto wallet will be called a hodler. The only difference between both is one has control of their crypto assets while the other doesn't have full crypto of their crypto assets
Holding in a non-custodial wallet is much safer compared to storing funds in exchanges. I don't know why some prefer to do that but for me that is risky as we all know it is inevitable for a specific exchange to get hacked so our funds will surely be compromised if that will happen just like what had happened to Bybit just recently. Though regardless of where we stored our funds we call it holding but long term is on another level.