What is the difference between :first-child and :first-of-type?

I have created an example to demonstrate the difference between first-child and first-of-type here.

    .parent :first-child {
      color: red;
    }

    .parent :first-of-type {
      background: yellow;
    }

    .parent p:first-child {
      text-decoration: line-through;
    }

    // Does not work
    .parent div:first-child {
      font-size: 20px;
    }
    // Use this instead
    .parent div:first-of-type {
      text-decoration: underline;
    }
    // This is second child regardless of its type
    .parent div:nth-child(2) {
      border: 1px black solid;
    }

<div class="parent">
      <p>Child</p>
      <div>Child</div>
      <div>Child</div>
      <div>Child</div>
    </div> 

A parent element can have one or more child elements:

<div class="parent">
  <div>Child</div>
  <div>Child</div>
  <div>Child</div>
  <div>Child</div>
</div>

Among these children, only one of them can be the first. This is matched by :first-child:

<div class="parent">
  <div>Child</div> <!-- :first-child -->
  <div>Child</div>
  <div>Child</div>
  <div>Child</div>
</div>

The difference between :first-child and :first-of-type is that :first-of-type will match the first element of its element type, which in HTML is represented by its tag name, even if that element is not the first child of the parent. So far the child elements we're looking at have all been divs, but bear with me, I'll get to that in a bit.

For now, the converse also holds true: any :first-child is also :first-of-type by necessity. Since the first child here is also the first div, it will match both pseudo-classes, as well as the type selector div:

<div class="parent">
  <div>Child</div> <!-- div:first-child, div:first-of-type -->
  <div>Child</div>
  <div>Child</div>
  <div>Child</div>
</div>

Now, if you change the type of the first child from div to something else, like h1, it will still be the first child, but it will no longer be the first div obviously; instead, it becomes the first (and only) h1. If there are any other div elements following this first child within the same parent, the first of those div elements will then match div:first-of-type. In the given example, the second child becomes the first div after the first child is changed to an h1:

<div class="parent">
  <h1>Child</h1>   <!-- h1:first-child, h1:first-of-type -->
  <div>Child</div> <!-- div:nth-child(2), div:first-of-type -->
  <div>Child</div>
  <div>Child</div>
</div>

Note that :first-child is equivalent to :nth-child(1).

This also implies that while any element may only have a single child element matching :first-child at a time, it can and will have as many children matching the :first-of-type pseudo-class as the number of types of children it has. In our example, the selector .parent > :first-of-type (with an implicit * qualifying the :first-of-type pseudo) will match two elements, not just one:

<div class="parent">
  <h1>Child</h1>   <!-- .parent > :first-of-type -->
  <div>Child</div> <!-- .parent > :first-of-type -->
  <div>Child</div>
  <div>Child</div>
</div>

The same holds true for :last-child and :last-of-type: any :last-child is by necessity also :last-of-type, since absolutely no other element follows it within its parent. Yet, because the last div is also the last child, the h1 cannot be the last child, despite being the last of its type.

:nth-child() and :nth-of-type() function very similarly in principle when used with an arbitrary integer argument (as in the :nth-child(1) example mentioned above), but where they differ is in the potential number of elements matched by :nth-of-type(). This is covered in detail in What is the difference between p:nth-child(2) and p:nth-of-type(2)?