facebook.com this is the long url and the short one for facebook is
fb.com so if I have a website with a keyword like database for example
englishdatabase.com and I want to make it shorter like
englishdb.com so does it affects my rank in google as duplicate content ? which one should I consider as the main website and redirects the other one to ?
Does [this] affects my rank[ing] in [G]oogle [regarding] duplicate content?
Duplicate content generally refers to substantive blocks of content within or across domains that either completely match other content or are appreciably similar. Mostly, this is not deceptive in origin. Examples of non-malicious duplicate content could include:
Discussion forums that can generate both regular and stripped-down pages targeted at mobile devices
Store items shown or linked via multiple distinct URLs
Printer-only versions of web pages
Duplicate content on a site is not grounds for action on that site unless it appears that the intent of the duplicate content is to be deceptive and manipulate search engine results.
Regarding redirection specifically, I would choose the shortened URL for the main site but you should know that englishdatabase.com could be considered in search results. A search engine may know "facebook" is a site called facebook.com but what is "fb"?
However, if you were able to register "englishdb.com", I would likely think this would be sufficient. It's short and snappy and despite the less than perfect "db", any shortcomings could likely be overcome by using the phrase "english database" strategically in accordance with good SEO practices.
Regarding duplicate content issues, you may find that even if you follow some canonization guidelines, Google holding duplicate content against you may not be the real issue. The real issue with multiple URLs may be that you have difficulty stopping Google or other search engines from indexing your site in a way you would not prefer. Every URL pointing to a piece of content is a potential gateway to that content and a search engine will likely at least consider listing each one.
In this Webmasters question, note that Wordpress was being used, which is a CMS that offers two links to each post. Thus, the original poster had a total of 8 address (including http:// and https://) that could potentially be listed in Google for each post. This seems like a recipe for a headache.
As a final note, often the reason to have a second URL is for purposes of separation. For instance, gmail.com for google.com and ymail.com for yahoo.com are aimed squarely at the mobile market since they are easier to type. Likewise, if a large organization needs to separate domains for ease of data retrieval, that is another common use. So having "englishdb.com" connect to "englishdatabase.com" to retrieve, say, english data, might make sense, but using it just to hold a second copy of "englishdb.com" seems counter-productive.