The thing you are missing is called the vocative case! It’s also the thing that Spartacus is missing!
Latin (and a bunch of other languages, but mostly not English) likes to alter the forms of words depending on what grammatical function they have in the sentence. (English mostly uses word order to accomplish this.) In Latin, the noun that is the subject of the sentence is always in the nominative case:
Dominus servum amat.
The master loves the slave.
(I’m sorry; it was the only verb I could think of.)
The word dominus (“master”) ends in -us because it is in the nominative case, and therefore the subject of the sentence. The word servum (“slave”) ends with -um because it is in the accusative case, and therefore it is the object of the verb amat (“he/she/it loves”). You could put those three words in whatever order you want – servum dominus amat, dominus amat servum, whatever – and they would still mean “the master loves the slave” as long as you don’t change the endings. (If you want to say that the slave loves the master, that’s servus dominum amat.)
But wait, you might say! You said something about the vocative case! So what’s that? And what’s this domine thing? Domine is the form that the word dominus takes in the vocative case. The vocative is the case you use when you are addressing someone directly, such as when you are using their name or title:
Domine, ama servum!
O master, love the slave!
If you wanted to command a master to love a slave (I know it’s a weird setup, but work with me here) and you wanted to specifically call them master, the form of the word you would use is domine. (If what you have is a mistress, domina is the form in both nominative and vocative.)
So basically the choice comes down to “I want to use a Latin word for master when my slave characters address their masters, and I’m just going to use the nominative form because we don’t have case endings in English, so what the hell” (the Spartacus approach) versus “I want to use a Latin word for master when my slave characters address their masters, and since I am going to be using Latin words I want to use the form that a Latin speaker would have used in direct address” (the fanfiction approach). Obviously I have my biases, but I don’t think that either of these are flat-out wrong, per se – especially with Latin and Greek, English often has both native-English-style and borrowed-style forms for the same word, like the plurals of fungus or aquarium or formula or whatever you think the plural of octopus is – but it’s really up to you and the effect you are going for.
Having said that, I should probably mention that everything I have said above is a filthy lie.
Oh, not the case endings. That part’s not a lie. The part that is a lie is the word dominus.
As @carminapossunt is even now helpfully pointing out to me, current evidence suggests that Roman slaves basically NEVER used the word dominus or domina to address their masters. The evidence we have from Roman comedy is that the word slaves used to address their masters, when they needed a word, was erus (vocative ere) or era. Which does also mean “master” but it’s not the same word. Really. No kidding. Dominus by the first century AD (which is later than Spartacus, but still) basically just means sir – like, a polite term of address you’d use for anybody. So essentially WE ARE ALL WRONG. (For further information, please consult Eleanor Dickey’s book Latin Forms of Address: From Plautus to Apuleius.)
I hope that helps!