<p>The two meanings don't seem all that distinct. If, in the definition of the 1st sense of "mixture", you take probabilities as probability densities &amp; sums as integrals, you get a mixture in the 2nd sense; if, in the definition of the 2nd sense, you allow <span class="math-container">$\theta$</span> to index a countable set of distributions, you get 
a mixture in the first sense. (And there seems to be a gap&mdash;what do you call it when <span class="math-container">$\theta$</span> indexes an uncountable set of distributions that don't constitute a parametric family?<sup>&dagger;</sup>) At any rate the crux of the distinction needs to be made more explicit.</p>

<p>Even if compound distributions are more properly viewed as an extension of mixture distributions rather than as a sub-class, I wonder whether it mightn't be better to let  <em>mixture</em> cover the general idea, &amp; <em>compound distribution</em> the particular case&mdash;practically, to refrain from removing the <em>mixture</em> tag when adding the <em>compound distribution</em> tag.</p>

<p>&dagger; Wikipedia doesn't help: the article on mixture distributions defines compound distributions as those where <span class="math-container">$\theta$</span> indexes a set of uncountable distributions; while the article on compound distributions defines them as you do.</p>
