I have a simple question regarding "conditional probability" and "Likelihood". (I have already surveyed this question [here](http://stats.stackexchange.com/questions/2641/what-is-the-difference-between-likelihood-and-probability) but to no avail.)

It starts from the wikipedia [page on likelihood](https://en.wikipedia.org/wiki/Likelihood_function). They say this:

[![enter image description here][1]][1]

Great! So in English, I read this as: "The likelihood of parameters equaling theta, given data X = x, (the left-hand-side), is equal to the probability of the data X being equal to x, **given** that the parameters are equal to theta". (**Bold is mine for emphasis**).

However, no less than 3 lines later on the same page, the wikipedia entry then goes on to say:

[![enter image description here][2]][2]

(Highlights in red are mine to show the source of the confusion). So, in the first image, we are literally told about a conditional probability of $P(x|\theta)$, but immediately afterwards, we are told that this is actually NOT a conditional probability, and should be in fact written as $P(X = x; \theta)$? 

So, which one is is? Does the likelihood actually connote a conditional probability ala the first image? Or does it connote a simple probability ala the second image? 

Thanks in advance.    

  [1]: https://i.sstatic.net/rbfZU.png
  [2]: https://i.sstatic.net/Jzq9j.png