لا when followed by a majzum verb means it is an imperitive sentence (an order not to do something). Just like a command (imperitive sentence ) has a majzum verb, a negative command also has a majzum verb after it.
Take the example of : لا تذهبْ laa tazhab means don't go.
When لا is followed by a marfoo verb (with damma, for example) it is a negative sentence. For example: هي لا تذهبُ (hiya laa tazhabo) means she is not going. This is a present tense negative sentence.
In these sentences a verb follows laa.
a noun may also follow laa. That is a negative nominal sentence. For example, laa waladun fil ghurfaa. There is no boy in the room.
As for maa ما it is usually used in the past tense sentence. For example, ما درستُ maa darasto, i did not study.
in addition to maa and laa, there are other words that make the sentence negative. Such as لَمْ and ليس .
لم has the same effect on the sentence as ما
That is it makes the sentence past negative. The difference is that لم is used with the present tense verb. So لم أدرس and ما درست mean the same thing: I did not study.
Another thing is that the verb after لم is majzoom (has a sukoon, for example).
Check out my Arabic course in the Arabic section, EZ arabic for beginners, that explain all of these very well.