Difference between embedded question and noun phrase


Inspired by [this
question](https://japanese.stackexchange.com/questions/83210/translation-of-a-
simple-sentence), I thought of two ways to talk about checking the truth of
something, though I think my question applies much more generally than with
just the verb 'to check'.

> 雪が溶けていることを確認した。  
>  雪が溶けているか(を)確認した。  
>  I checked to see if the snow had melted.

My suspicion is that in the first sentence I am making the assumption that the
snow has melted and I am simply verifying my assumption. Whereas, in the
second sentence, I have no initial theory on what the result will be.

Are my sentences both valid? Is my theory correct? What did I get wrong?

