<h1>TL;DR:</h1>

<ul>
<li>I have added a tag wiki and an excerpt to <a href="https://stats.stackexchange.com/questions/tagged/compound-distributions" class="post-tag" title="show questions tagged &#39;compound-distributions&#39;" rel="tag">compound-distributions</a>. The excerpt notes that these are also known as "mixtures", but that that term also has other uses.</li>
<li><p>I have included a warning in the tag wiki excerpt for <a href="https://stats.stackexchange.com/questions/tagged/mixture" class="post-tag" title="show questions tagged &#39;mixture&#39;" rel="tag">mixture</a>. It now reads:</p>

<blockquote>
  <p>A mixture distribution is one that is written as a convex combination of other distributions. Use the "compound-distributions" tag for "concatenations" of distributions (where a parameter of a distribution is itself a random variable).</p>
</blockquote>

<p>I will link to this meta question in the tag wiki.</p></li>
<li><p>I will go through threads with the <a href="https://stats.stackexchange.com/questions/tagged/mixture" class="post-tag" title="show questions tagged &#39;mixture&#39;" rel="tag">mixture</a> tag in the next days and retag them as <a href="https://stats.stackexchange.com/questions/tagged/compound-distributions" class="post-tag" title="show questions tagged &#39;compound-distributions&#39;" rel="tag">compound-distributions</a> as warranted.</p></li>
</ul>

<hr>

<h1>Explanation:</h1>

<p>The term "mixture" has two distinct meanings in our context:</p>

<ul>
<li>A <em>mixture distribution</em> is a convex combination of two or more underlying distributions with associated probabilities <span class="math-container">$p_i$</span> that sum to one. A realization of the mixture distribution comes with probability <span class="math-container">$p_i$</span> from the <span class="math-container">$i$</span>-th underlying distribution. Examples include:

<ul>
<li>The mixture of two or more normal distributions with different means and/or variances: <a href="https://stats.stackexchange.com/questions/tagged/gaussian-mixture" class="post-tag" title="show questions tagged &#39;gaussian-mixture&#39;" rel="tag">gaussian-mixture</a>s.</li>
<li>The mixture of a point mass at zero with another (discrete) distribution: <a href="https://stats.stackexchange.com/questions/tagged/zero-inflation" class="post-tag" title="show questions tagged &#39;zero-inflation&#39;" rel="tag">zero-inflation</a>.</li>
</ul></li>
<li>A <em>mixture</em> may also be a "concatenation" of two distributions (<a href="https://stats.stackexchange.com/questions/tagged/compound-distributions" class="post-tag" title="show questions tagged &#39;compound-distributions&#39;" rel="tag">compound-distributions</a>), where our realizations are distributed according to some parameterized distribution <span class="math-container">$X\sim F_\theta$</span> where the parameter <span class="math-container">$\theta$</span> itself is a random variable, <span class="math-container">$\theta\sim G$</span>. So, to draw an <span class="math-container">$x$</span>, you first draw a <span class="math-container">$\theta\sim G$</span> and then, with this <span class="math-container">$\theta$</span>, draw <span class="math-container">$x\sim F_\theta$</span>. <span class="math-container">$G$</span> is called the <em>mixing distribution</em>. Examples include:

<ul>
<li>The <a href="https://stats.stackexchange.com/questions/tagged/negative-binomial" class="post-tag" title="show questions tagged &#39;negative-binomial&#39;" rel="tag">negative-binomial</a> distribution arises naturally as a Poisson distribution whose parameter is itself gamma distributed: it is a "Poisson-gamma mixture".</li>
</ul></li>
</ul>

<p>It does not help that even when people discuss compound distributions as such, they almost invariably call the resulting compound distribution an "<span class="math-container">$F$</span>-<span class="math-container">$G$</span> mixture", as in the negbin case (not, e.g., an "<span class="math-container">$F$</span>-<span class="math-container">$G$</span> compound"). Ah well.</p>

<hr>

<p>Our <a href="https://stats.stackexchange.com/questions/tagged/mixture" class="post-tag" title="show questions tagged &#39;mixture&#39;" rel="tag">mixture</a> tag refers exclusively to the first meaning above. Here is its tag wiki excerpt:</p>

<blockquote>
  <p>A mixture distribution is one that is written as a convex combination of other distributions. </p>
</blockquote>

<p>The overloaded nomenclature results in people tagging questions as <a href="https://stats.stackexchange.com/questions/tagged/mixture" class="post-tag" title="show questions tagged &#39;mixture&#39;" rel="tag">mixture</a> when they are actually asking about mixtures in the second sense above, i.e., about <a href="https://stats.stackexchange.com/questions/tagged/compound-distributions" class="post-tag" title="show questions tagged &#39;compound-distributions&#39;" rel="tag">compound-distributions</a>.</p>

<p>The "disambiguation" section of the <a href="https://stats.stackexchange.com/questions/tagged/mixture" class="post-tag" title="show questions tagged &#39;mixture&#39;" rel="tag">mixture</a> tag wiki only disambiguates it from mixed models.</p>

<hr>

<p>Any thoughts, comments or improvements on the tag wikis would be more than welcome.</p>
