What is the difference between display: inline and display: inline-block?

One thing not mentioned in answers is inline element can break among lines while inline-block can't (and obviously block)! So inline elements can be useful to style sentences of text and blocks inside them, but as they can't be padded you can use line-height instead.

<div style="width: 350px">
  Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua.
  <div style="display: inline; background: #F00; color: #FFF">
    Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat.
  </div>
  Duis aute irure dolor in reprehenderit in voluptate velit esse cillum dolore eu fugiat nulla pariatur. Excepteur sint occaecat cupidatat non proident, sunt in culpa qui officia deserunt mollit anim id est laborum.
</div>
<hr/>
<div style="width: 350px">
  Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua.
  <div style="display: inline-block; background: #F00; color: #FFF">
    Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat.
  </div>
  Duis aute irure dolor in reprehenderit in voluptate velit esse cillum dolore eu fugiat nulla pariatur. Excepteur sint occaecat cupidatat non proident, sunt in culpa qui officia deserunt mollit anim id est laborum.
</div>

display: inline; is a display mode to use in a sentence. For instance, if you have a paragraph and want to highlight a single word you do:

<p>
    Pellentesque habitant morbi <em>tristique</em> senectus
    et netus et malesuada fames ac turpis egestas.
</p>

The <em> element has a display: inline; by default, because this tag is always used in a sentence. The <p> element has a display: block; by default, because it's neither a sentence nor in a sentence, it's a block of sentences.

An element with display: inline; cannot have a height or a width or a vertical margin. An element with display: block; can have a width, height and margin.
If you want to add a height to the <em> element, you need to set this element to display: inline-block;. Now you can add a height to the element and every other block style (the block part of inline-block), but it is placed in a sentence (the inline part of inline-block).

A visual answer

Imagine a <span> element inside a <div>. If you give the <span> element a height of 100px and a red border for example, it will look like this with

display: inline

display: inline-block

display: block

Code: http://jsfiddle.net/Mta2b/

Elements with display:inline-block are like display:inline elements, but they can have a width and a height. That means that you can use an inline-block element as a block while flowing it within text or other elements.

Difference of supported styles as summary:

• inline: only margin-left, margin-right, padding-left, padding-right
• inline-block: margin, padding, height, width