To add to the info that Nathan has already provided;
The WEBID used to be the only way to log-in to the panel and you could choose your own WEBID during the sign-up process. Sometime last year DreamHost added the ability to log-in using the email address listed in your account profile, at around the same time they started to auto-generate the WEBIDs instead of allowing customers to choose their own.
Basically, WEBIDs are being deprecated (or phased out) for customer use, replaced by the email address and an account number (as used in affiliate links), but I believe WEBIDs are still used for internal DreamHost purposes.
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