Are all AC adapters the same size?

I have a Brookstone Iphone dock/speakers that is not sold anymore, and the power adapter is broken. I'm going to buy another one, but I'm not sure if it matters which one to get. First of all, the plug for the adapter itself says AC adapter, but on the speakers themselves, it says input: DC. I have tried a couple of adapters that I found around my house that look very similar, but the size is slightly off, so they do not fit. The current adapter I have says Output: 10V==3.4A. Will any 10V adapter I get fit the speakers or will I need a specific size? Also, what is the difference between and AC and DC adapter and which one should I get?

You need the right voltage, or at least close. You need the right polarity. And you need at least as much current as the device uses. And you need DC not AC. If you get any of that wrong, it won't work properly and has a good chance of being permanently damaged.
And then you need the right size plug, too.
You can buy multi-voltage supplies with swappable plugs, then you
set the voltage to whatever is printed on the speakers.
I don't know of any electronics that actually uses AC. They all use DC inside. So you can get an AC-DC converter to run a device off household AC supply 110V-240V, and you can get a DC-DC converter to run it off a 12V DC car outlet.