Strange question tbh.
You can register a e-mail adress to your account at the runescape site. So you log in with your account on the site, then you browse trough some tab pages about account recovery, and their you can set a e-mail adress for your account.
When it then gets hacked in the future (or forget password or other reason for not having it) you can enter the e-mail adress and you can then change password. That has nothing to do with appealing. Appealing and email recovery are both different things. E-mail can be used if you were smart enough to set one, appealing is usefull if you were to stupid to set one and you would have to experience the painfully process of answering the recovery questions + other info.
The other account probably hadnt a e-mail registered. You always have to manually register an email to a account. If you forgot this, the account has no known registered e-mail adress and the only way to recover it will be trough appeall recovery which is a painfully process full of uncertainties. The runescape site wont tell you if there was a e-mail registered to that account at all (unless when u log in which you cant) just like runescape will never tell you in the appeal if you had set recovery questions. All open options, jagex is quite harsh in these activities. You should simply write everything down thats important to your account. Which is a mistake i oftenly make.
So the question is...
Are you completely sure you have had e-mail registered to both you accounts (both different emails???) cause if you havent at one of them it will not be able to be recovered trough mail, painfull but simple. The e-mail recovery is a automatic system and should detect yours rightfully e-mail.