For URLs in browsers, http://www.example.com/ and http://www.example.com are the same URL. Whether or not the trailing slash is shown in the browser address bar is purely cosmetic - when the request is sent to the server the slash will be included. (http://www.example.com/foo and http://www.example.com/foo/ on the other hand are different URLs.)
The following is a very good explanation, taken from Stack Overflow: Trailing slash in URLs - which style is preferred?
In my personal opinion trailing slashes are misused.
Basically the URL format came from the same UNIX format of files and folders, later on, on DOS systems, and finally, adapted for the web.
A typical URL for this book on a Unix-like operating system would be a file path such as file:///home/username/RomeoAndJuliet.pdf, identifying the electronic book saved in a file on a local hard disk.
Source: Wikipedia: Uniform Resource Identifier
Another good source to read: Wikipedia: URI Scheme
According to RFC 1738, which defined URLs in 1994, when resources contain references to other resources, they can use relative links to define the location of the second resource as if to say, "in the same place as this one except with the following relative path". It went on to say that such relative URLs are dependent on the original URL containing a hierarchical structure against which the relative link is based, and that the ftp, http,
and file URL schemes are examples of some that can be considered hierarchical, with the components of the hierarchy being separated by "/".
Source: Wikipedia Uniform Resource Locator (URL)
That is the question we hear often. Onward to the answers! Historically, it’s common for URLs with a trailing slash to indicate a directory, and those without a trailing slash to
denote a file:
http://example.com/foo/ (with trailing slash, conventionally a directory)
http://example.com/foo (without trailing slash, conventionally a file)
Source: Google WebMaster Central Blog - To slash or not to slash
A slash at the end of the URL makes the address look "pretty".
A URL without a slash at the end and without an extension looks somewhat "weird".
You will never name your CSS file (for example) http://www.sample.com/stylesheet/ would you?
BUT I'm being a proponent of web best practices regardless of the environment.
It can be wonky and unclear, just as you said about the URL with no ext.