what is the difference between self and this? [duplicate]

I have the following two codes:

<?php
class pagamentos {
  public $tipo = array('avista', 'aprazo', 'outros');

  function fPag($type) {
    return in_array($type, $this->tipo);
  }
}

This way I would use this as follows:

<?php
$cPagamentos = new pagamentos();
if ($cPagamentos->fPag('avista')) {
  // É uma forma válida
}

My classmate did the same procedure, but in a different way:

<?php
    class pagamentos {
      public static $tipo = array('avista', 'aprazo', 'outros');

      function fPag($type) {
        return in_array($type, self::tipo);
      }
    }

Used differently:

<?php
if ($cPagamentos::fPag('avista')) {
  // É uma forma válida
}

What I realized was that in his case, he did not need to instantiate the object.

• Is there a difference in memory allocation between these two forms of use?
• What is the theoretical difference between self and $this in these 2 functions?

I've researched, but I ended up getting confused more and I did not understand the concept.