The short answer is that it's complicated. Linguists today take very seriously the distinctions between American English and Black English, or AAVE. But since the speakers of each dialect tend to understand each other and live in close proximity we say that they speak two dialects of the same language. But the linguistic differences are not insignificant especially when you take into account the distinctive (and regular) use of verb tenses.
From a statement by the "Linguistics Society of America" in 1997...
" 1) The variety known as "Ebonics," "African American Vernacular English" (AAVE), and "Vernacular Black English" and by other names is systematic and rule-governed like all natural speech varieties. In fact, all human linguistic systems -- spoken, signed, and written -- are fundamentally regular. The systematic and expressive nature of the grammar and pronunciation patterns of the African American vernacular has been established by numerous scientific studies over the past thirty years. Characterizations of Ebonics as "slang," "mutant," "lazy," "defective," "ungrammatical," or "broken English" are incorrect and demeaning.
"2) The distinction between "languages" and "dialects" is usually made more on social and political grounds than on purely linguistic ones. For example, different varieties of Chinese are popularly regarded as "dialects," though their speakers cannot understand each other, but speakers of Swedish and Norwegian, which are regarded as separate "languages," generally understand each other. What is important from a linguistic and educational point of view is not whether AAVE is called a "language" or a "dialect" but rather that its systematicity be recognized."
Wikipedia has a good description of some of the more interesting differences about halfway down the page under the heading "Tense and Aspect."