Wordpress Theme and Widget Question

[2BB]

I can't remember if I asked this question before but here goes...

If I change the content in my widgets for one theme, will it affect another theme or are all themes independent??

I have a theme that's all setup widget wise and is showing on my website, but I also have another one I'm thinking about swapping it for. Right now it looks like I will have to do a little content rearranging to get the 2nd theme to look right.

Any help will be appreciated! Thanks!

[dojo]

I think the new skin should be set with widgets too. I recall they worked on some and not on others ...