A domain is for example http://yoursite.com
A subdomain is.. http://subdomain.yoursite.com
And a page can be anything from
http://yoursite.com/index.html
http://yoursite.com/details.html
http://yoursite.com/details/page1.html
http://subdomain.yoursite.com/details/page1.html

As far as which way you should do it, it is up to you. Search engines will treat a subdomain as its own site, that could be good or bad depending on what you are trying to achieve.

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