Wagon and waggon are different spellings of the same word, though the shorter one is preferred in all modern varieties of English. Waggon was preferred in British English until a century ago,1 and it still appears occasionally, but it is fast becoming archaic.
Examples
Wagon is standard in American English””for example:
Paddle shifters in a station wagon would seem at first glance about as necessary as a roof rack on a convertible. [Charleston Post Courier]
Becoming frightened while on Meyer Street, a horse attached to a milk wagon ran away while the driver was delivering milk. [Arizona Daily Star]
And while waggon used to be the standard spelling in British English, wagon is now far more common. For example, these major British publications use it:
Toyota hopes to capitalise on the recent uptick with the unveiling of a wagon-type version of its popular Prius hybrid hatchback at the Detroit car show next Monday. [Financial Times]
The sooner you fall off whichever wagon you tipsily clambered aboard at the strike of midnight, the sooner you can begin to ring in the real changes. [Guardian]
References
1. Google Ngram charting use of “wagon” and “waggon” in British books from 1800 to 2000 ^
