Differential Object Marking

Some languages, such as Russian, Turkish, Finnish and Hebrew, have a thing known as differential object marking. English, to some extent, can also be said to have it, although in a less predictable, unsystematic form.

In these languages, the direct object gets a different marking depending on some grammatical distinction. In Turkish and Hebrew, direct objects are normally marked identically to subjects, but when the object is definite, it is marked with an object marker. -yi|-yı|-yü|-yu in Turkish, et- in Hebrew.

In Finnish, the object is slightly more complicated, and the distinction that is made is not primarily one of definiteness. If the action is negated, the object is marked with the partitive case:

minä e-n siedä kylmää vettä

I not-1SG tolerate cold-PART water-PART

I can't stand cold water

This holds regardless of the aspect of the verb. If the verb is positive, and atelic, you also get the partitive:

aja-n auto-a

drive-1SG car-part 

I am driving (the|a) car

However, if the verb is telic and positive, the object is marked by the accusative:

aja-n auto-n auto-talli-in
drive-1sg car-ACC car-stable-INTO
I('ll) drive the car into the garage (implicitly, this is mentioned with the result in mind, or as something that will be completed before the speaker goes on to the next thing he's about to do)

hän rakentaa talon valmiiksi ensin

3SG build-(3sg) house-ACC ready-TRANSL first-INSTR

he will build the house (to completion) first*

* in the sense of 'before doing something else'

One context in which such completion is pretty central is when giving the order in which events are to happen:

syö-n ruoa-n ja sitten tule-n muka-an

eat-1sg food-ACC and then come-1sg with-TO

I'll eat food and then I'll come

c.f. the case marking in a less time-ordered utterance:

älä nyt, syö-n ruoka-a

don't_IMPER now, eat-1SG food-PART

stop doing that, I'm eating food

So basically, when the completion of the action is relevant, and it is a positive utterance, it's accusative, otherwise it is partitive. There's further complications with regards to the marking of the accusative, but that is syntactically predictable. 

Other similar systems exist in languages around the world, and looking at one particular part of English grammar might be relevant.

C.f. 

I shot the bear vs. I shot at the bear

The former implies that the bear, in fact, was hit (and probably died), whereas the latter tells us that the shooting was a failure. Many English verbs seem to have similar pairs, where the prepositionless version is more telic and successful, whereas the version with the preposition generally is less telic, less successful. However, different verbs seem to have different prepositions in use, and just a few exceptional ones seem to have the opposite situation - a preposition makes the verb more telic, c.f.

eat vs eat up

 However, in English, some of these verbs permit this even without an explicit object, so whether it's object marking or just 'marking' is a bit unclear.