Indeed, there are two different meanings. These different meanings can be expressed by the same Hungarian sentence, depending on the context, and both Hungarian sentences required accusative. See below for an explanation.
I wait a lot - I wait a long time because the flight is delayed
I wait for a lot - I expect, my expectations are high
And back to the original question, why "sokat", instead of "sok".
It should be applied many times different grammatical case/phrasal verb/preposition in the English and the Hungarian language.
In the Hungarian language, nouns, pronouns, adjectives, verbs (yes verbs, too) and their affixes (suffixes) take different inflected forms depending on what case they are in. The accusative of inflective languages (as the Hungarian) is one of the grammatical cases what answered that "whom?" or "what?"question; that is to say a word or phrase expresses the structure that fills the role of the object in a sentence.
Languages such as Hungarian have extensive case systems, with nouns, pronouns, adjectives, and determiners all inflecting (usually by means of different suffixes) to indicate their case. The Hungarian has eighteen grammatical cases. A role that one of these languages marks by case will often be marked in English using a preposition. The English prepositional phrase "for" might be rendered in Hungarian using the accusative case, such as in the above sentence.
This is an adverb in English, but in Hungarian accusative, since it answers the "mennyit?" question. (Mennyi? means how many) The Hungarian has the question "how many?" in accusative as well: mennyit? Mennyit várok? Sokat. As I explained, it should be applied many times different grammatical case/phrasal verb/preposition in the English and different in the Hungarian language. The accusative case long ago exsisted in all Indo-European languages, but eg. from English it essentially disappeared. The English preserved it only the "whom?" interrogative word and some personal pronoun. I think that is why it is so hard to understand why many word requires the accusative in other languages when they don't required in English.
Sometimes things are used as adverbs in some languages and as nouns in others, and we have to accept it ;) For example, the way we express speaking a language: HU 'magyarul beszél (adverb)', DE 'Deutsch sprechen' (noun) / 'deutsch sprechen' (adverb), FR 'parler français (adverb) / parler le français (noun)'.
When it comes to time words (and other) being declined in the accusative, I saw it described as 'adverbial accusative'.
I believe that both are valid depending on context. when using the accusative case with varni it often applies to time, but can be used for expectation at well.
Sokat varok I'm waiting for a lot (expectation) I am waiting a lot (time)
Take these two examples from a magyar angol szotar (dictionary)
1) 20 percet vartunk a buszra - we waited twenty minutes for the bus
Here the accusative case is on the ammount of time, and the expectation uses the "-ra/re" (onto)
2) varok valakit a repeloteren - I am waiting for someone at the airport.
Here the accusative case is use for the expectation of someone. rather than a time amount.
A better question might be what question would prompt each response. Adda's response clearly states the expectation response, (Waiting for a lot) but I can't think of a good example for time at the moment. I would love to hear others insights.
I can hardly imagine a context where "Sokat várok" could mean "I wait for a lot", is "a lot" such a thing that you can wait for? I admit I could imagine "I expect a lot" as a valid translation but with waiting, I would expect something concrete for an argument... at least for the Hungarian version; I don't know.
I believe it would be :
I am waiting a lot for a car : Sokat varok egy autora (here the quantity a lot is the object, so it gets the accusative t, and in hungarian you use the suffix -ra,-re with the verb varni to wait for something for an amount of time)
I am waiting for a lot of cars: sok autot varok. (Here sok is being used as an adjective not the subject, so it doesn't need an accusative t. Here I'm not sure which would be more proper, sok autot varok or sok autora varok. My dictionary seems to place either as acceptable.
There's no time frequency indicated in the sentence, just that "I wait a lot." What you are waiting for isn't mentioned, so you could be waiting for something not just for a long time. You also be saying that you have high expectations (which is the same phrase,) in which case the "for a long time," would be completely misplaced. Hope that helps :)