Aliases: difference between .bash_rc, .bash_aliases and /usr/local/bin

With the first method you are not creating an alias, you are creating a symlink. Symlinks are short for symbolic links:

Symbolic links are files that act as pointers to other files. [...] A symbolic link is a special type of file whose contents are a string that is the pathname another file, the file to which the link refers. In other words, a symbolic link is a pointer to another name, and not to an underlying object.

Read more about symlinks here and here.

Only with the second method you are, in fact, creating an alias.

Aliases allow a string to be substituted for a word when it is used as the first word of a simple command. The shell maintains a list of aliases that may be set and unset with the alias and unalias builtin commands (see SHELL BUILTIN COMMANDS below). The first word of each simple command, if unquoted, is checked to see if it has an alias. If so, that word is replaced by the text of the alias.

You can define an alias anywhere where you can type a command and have the shell (bash in this case) interpret it, however in order for the alias to be available in other shells it needs to be defined in a file that's interpreted by the shell on startup (shell startup, not computer startup).

For bash these are /etc/bash.bashrc (system wide) and ~/.bashrc. These files are interpreted when the shell starts in interactive mode (like when using Terminal). I'm not going to mention the profile files because they serve a different purpose.

So, you want to add your aliases to ~/.bashrc to have them available in every interactive shell.

The .bash_aliases method accomplishes exactly the same thing as putting the aliases in ~/.bashrc but has the added benefit of being easier to be parsed and manipulated by programs.

The . ~/.bash_aliases means source (load) _~/.bash_aliases_ in the context of the currently running shell.