Ubuntu – variable expansion in single quote

I've tried to break this down a little bit for you, using your own examples/text as well, check it out:

$ cat fred    
#!/bin/bash

fred='Four spaces between these    words.'

echo "The value of \$fred is $fred"

echo "The next line being printed is simply the results of # echo \$fred"

echo $fred

Running the bash script above prints the following to the terminal/stdout:

The value of $fred is Four spaces between these    words.
The next line being printed is simply the results of # echo $fred
Four spaces between these words.

As well, you can view a terminal video of this here: http://showterm.io/98f56243f60551b338b9f

• echo $'$foo': the $'[...]' token around $foo interprets $foo literally (as $foo) and tries to expand ANSI C-like escape sequences in it, which are not present, so echo yields $foo;
• echo $"$foo": the $"[...]" token around $foo expands $foo to its value (pwd) and tries to translate it if the current locale is not POSIX / C; this is not happening, because either the current locale is POSIX / C or a translation for pwd is not available, so echo yields pwd;
• echo $`$foo`: the `[...]` token around $foo allows the expansion of $foo, so $foo is expanded to its value (pwd); the expanded value is run in a subshell, whose output (~/scripts) replaces the whole `[...]` token, so echo yields the $ token followed by the ~/scripts token ($~/scripts).

Ultimately, the last one prints $~/scripts because $`foo` is a combination of a literal $ followed by a command substitution; so the leading $ is interpreted as a literal $ and the trailing `$foo` as a command substitution.