In HTML5, the preferred standard, the strong tag is recommended for important text. This is almost always displayed as bold text in browsers. Place the text you want bolded in between these tags: <strong>bold text here</strong>. "Headings" are usually placed at the top of the web page or at the beginning of a new section. Usually, headings are displayed as bold and larger than the regular font, but this can vary. There are six different heading tags, from <h1> to <h6>. Follow these guidelines when using them:  The h1 tag, written <h1>Your Heading Here</h1> is the most important heading, typically the largest text at the top of the page. <h2>The h2 tag</h2> is for the second most important heading, and so on down to <h6>h6, the smallest</h6>. Use these sparingly, only to organize your page. Users should be able to skim the headings quickly and find the topic they're looking for. When creating subheadings, move down just one level at a time. In other words, don't skip from <h1> to <h3>. This helps the HTML page preserve its formatting when transferred to another format. The <b> tag is still supported in HTML5, but <strong> is preferred in most situations. Use the <b> tag only when the text should be bolded for stylistic reasons, not to add emphasis. Examples include key words or vocabulary words in a passage, or product names in a review. As with most tags, <b>place the affected text between a start tag and an end tag</b>.

Summary:
<strong>Use the strong tag</strong>. Use heading tags instead when appropriate. <b>Use the b tag as a last resort</b>.