Difference between Domain , Sub-Domain & Sub-Directory

Definitions

The following are a few common definitions to facilitate our discussion:

Domain

Definition: “The first-level set of domain names are the top-level domains (TLDs), including the generic top-level domains (gTLDs), such as the prominent domains com, net and org, and the country code top-level domains (ccTLDs). Below these top-level domains in the DNS hierarchy are the second-level and third-level domain names that are typically open for reservation by end-users that wish to connect local area networks to the Internet, run web sites, or create other publicly accessible Internet resources.” (source: Wikipedia)
Example: http://how-to-blog.tv or http://www.orangecaster.com (note: the subdomain shows up between the http:// and the domain name in the second example.)
Page Rank: Though Google tracks page rank at the actual “web page level” a domain can be considered the equivalent of your social security number on the web as all pages and page rank are generally associated with a domain. (see below for more details)

Subdomain

Definition: “The Domain Name System (DNS) has a tree structure or hierarchy, with each node on the tree being a domain name. A subdomain is a domain that is part of a larger domain, the only domain that isn’t also a subdomain is the root domain.[1] For example, “mail.example.com” and “calendar.example.com” are subdomains of the “example.com” domain, which in turn is a subdomain of the “com” top-level domain (TLD)”. (source: Wikipedia)
Example: hhttp://blog.macsales.com/ (note that How-To-Blog.TV has no “www” meaning our blog doesn’t even have the common subdomain of www associated with it.)
Page Rank: Since each subdomain is treated as a different domain, subdomains will not share page rank with the website. However you can link between the website and subdomain and leverage your page rank this way. It does take time for the “link juice” to pass.
Search Engine Results: Again each subdomain is considered its own website so your search engine results could include one to two results for each subdomain right? Wrong, Google now treats subdomains the same as folders for their search results. (source: SEO Round Table

Subdirectory

Definition: Folder, directory, catalog, or drawer, in computing, is a virtual container within a digital file system, in which groups of computer files and other folders can be kept and organized. (source: Wikipedia)
Example: http://www.orangecaster.com/social-media (our general marketing blog at Orangecast is installed in a subdirectory)
Page Rank: Since the subdirectory shares the same domain name, the page rank is distributed to it from the rest of the website.
Search Engine Results: Matt Cutts explains what Google calls host crowding in this post on subdomains and subdirectories. The basic idea is that in most cases Google will only show two results from one hostname. Since the subdirectory will sit at the end of the hostname it will compete with the rest of your website to be one of the two results.