You're not listening very well. I think you should consider attending some electronics courses, preferably not online, since you need handholding and a live person to ask questions to. I say this because rather than absorb the information, you have a tendency to want to challenge the information given. It's good to want to learn more about electronics but you should do it in a true educational forum (and I don't mean internet forums) so that you will learn the correct information rather than get information from a group where few of the members have formal instruction in the discipline. This is not a dig, it is a suggestion. But if you really want to get your information from internet forums, then don't get it here, go to AllAboutCircuits (and a few others) where many if not most of the members are professional electronics engineers and electricians that will give you the educational experience you want. Just be advised that you will be expected to do your own research as they are not there to conduct free electronics classes but will gladly answer specific questions. If you ask a question where the response is going to begin with...... "where do I begin...." you know you are in trouble. Nobody wants to waste time educating someone that just sits there and says give it to me because I'm too lazy to find this information myself.
As for the 777, there IS NO 18v rail. There is a 15v unregulated rail regardless of how the boombox is powered up. There are a few "regulated" internal rails but they are there to supply power to voltage sensitive circuits such as for the tuner, which due to precise circuit tuning, requires a stable supply. The AC P/S is not regulated but if it were, I suspect that it would be "regulated" at about 15volts. The expected "average" or normal voltage during AC usage will probably be around 15-16 volts anyhow. Forget the 18.1 volts no-load measurement, it's meaningless. And the AC input is not there for show... it is the transformer's input rating. Unity gain is the best you can hope for with respect to power and zero loss (or 100% efficiency) which we know isn't really possible, especially with unregulated linear supplies. So with that, the 61 watts (or whatever the back of your boombox case says) is the rated continous power consumption. That gives you 15v @ approx 4-amps. Higher current draw will result in a corresponding reduction in voltage = approx same "power."
One last thing.... please stop quoting text when you respond unless absolutely necessary or if you are responding to a particular point in which case, only quote the necessary applicable text. We here on this forum are not so stoopid that we don't know what you are responding to, especially if there's only 1 other post. Thanks.