putting something into single quotes in a bash script

[Petrus de Calguarium]

What is the difference in a bash script when one places something between 
single quotes:

- using the apostrophe, '
- using the accent grave, `

?

Eg.,

ps -fu 'whoami'
ps -fu `whoami`

They produce entirely different results.

There are many other places where one might wish to put a command, variable, 
etc., into single quotes, so, which type of single quote sahould be used and 
what is the diffence between the two?