What are the differences between "Ya Allah" vs "Allahuma"?

I have a little but not much knowledge of Arabic. Although **God** is called `Al-Karim, I hear the invocation Ya Karim, but I never heard the invocation Ya Al-Karim or Ya-l-Karim. Same for other names of **God**: the definite article disappears from the vocative. Just as it would in English: May the Lord have mercy on us vs. O Lord, have mercy on us` One big exception: `Ya Allah, which I've heard lots. (With definite separation between the end of Ya and the start of Allah, there are three different "a" sounds. I'm not talking about yalla as in let's go`.) Now I see that when my English translation of the Quran has `O God, the original is Allahuma`. I don't know anything like this construction, where someone is addressed by tacking "-uma" at the end or something similar. Though as I say, I'm not at all knowledgeable in Arabic and might easily have missed something. So is there a difference? Is `Ya Allah in the Quran and I missed it? Is Allahuma preferred? Is Allahuma` a unique construction?