"Drunk" is the plain, simple, direct, basic word.
"Plastered" is one of a many of words and phrases that mean "very drunk." Other words include "stewed," "stinko," "smashed," "liquored up," "tight," and literally dozens of others. They are all informal, colloquial.
"Drunk" because of being direct and plain is negative. Formal words that might be used, for example, in a police report include "intoxicated," "inebriated," and "under the influence."