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-J
If you have both domains, I suggest using an HTTP status 301 redirect from one to the other.
For Google listings, I suggest following FleaPit's suggetion and picking different pages of content for different phrases.
This is always difficult. You don't want to duplicate content... ie, you don't want two pages whose only difference is the spelling of your target word. This is bad for the engines and bad for users. You also don't want to appear illiterate.
I'm in a situation right now where research shows that a targeted brand name is misspelled on the web twice as often as it's spelled correctly. Let's say that Brandent is the correct spelling, but Brandant is searched more often. On pages where the brand name is a part of the target, after much discussion, we've decided to go with page titles in this form...
Brandent/Brandant Widgets
This acknowledges the problem right off... puts the correct spelling first... and gives us an exact match on "Brandant Widgets," which is the more competitive form. On the page, we're favoring the correct spelling, but we're covering our bases for both.
I don't use "Brandent/Brandant" on the page, but I have exact matches for both "Brandent Widgets" and "Brandant Widgets." Probably, because of this dual targeting, I'll have more uses of "widgets" on the page than I'd like. This dual targeting on one page more difficult to do if your phrases are very competitive... you may then have to build separate pages, with unique content.
Somewhere I remember somebody suggesting introducing the misspelling by saying, "No matter how you spell it..." Depends on the style of the site.
I don't know what you'd find if you tried searching for the topic here via Google, but you might turn up some good threads... there have been a lot of them. Try a search for:
mispellings site:webmasterworld.com
I have at least 6 of my keywords with different spellings. They are all very important keywords and critical to the success of the site. On the index page, I have used both spellings for two of the most important keywords and weighted them similarly.
The really big problem comes into play when there are not only two different spellings ... but people frequently spell both incorrectly! :)
There is enough information on the site that I have been able to target each of the different spellings for different pages of content.
Don't worry, people aren't stupid. They will recognize that if you have spelled a word one way on one page and another way on a different page ... that it was likely done in order to pull traffic from both sectors of the population using both correct spellings. (They won't think you are a moron who can't spell!)
Just write some really good content and target one or two keywords per page. The rest should take care of itself.
