:focus and :active are two different states.
:focusrepresents the state when the element is currently selected to receive input and:activerepresents the state when the element is currently being activated by the user.
For example let’s say we have a <button>. The <button> will not have any state to begin with. It just exists. If we use Tab to give “focus” to the <button>, it now enters its :focus state. If you then click (or press space), you then make the button enter its (:active) state.
On that note, when you click on an element, you give it focus, which also cultivates the illusion that :focus and :active are the same. They are not the same. When clicked the button is in :focus:active state.
An example:
<style type="text/css">
button { font-weight: normal; color: black; }
button:focus { color: red; }
button:active { font-weight: bold; }
</style>
<button>
When clicked, my text turns red AND bold!<br />
But not when focused only,<br />
where my text just turns red
</button>
edit: jsfiddle