I have an ecommerce site with an online community on a different subdomain. The community ranks for different keywords. If I would move the community to a different domain would that impact the SEO of the ecommerce site in any meaningful way?
It may impact your rankings as the sub-domain is part of your main domain. It's content could be helping your rankings. Is the communities overall purpose focused around the products you are selling? If so you may want to create sub-forums if you're running a forum and moderate threads to be kept on topic.
I know of a few websites which have forums on sub-domains and i'm sure it's helping with sales. I'd try and use the forum to generate more sales. Send targeted emails to members, put up relevant ads within different forums and threads etc. But I would not remove it from my site if the initial reason was to have a forum related to my products.
For the keywords rating/calculations - every subdomain can be separate item as with the main domain. Most of search engines allow separate sitemap file for every subdomain you wish to submit to them (Goggle Webmaster Tools, Bing/Yahoo Webmaster Tolls, etc.).
The website traffic ranking (Alexa etc) is different - there website item/record covers the main domain and all added subdomains.
In other words the best solution is to stay on subdomain - as it will keep separate the keywords rating (in Search Engines), and will combine/increase the whole website traffic ratings.