Dialects and accents are completely two different things. An accent is just a different way to pronounce the native language, whereas a dialect is almost a different language in itself, complete with different words and pronunciations altogether which are incomprehensible to all non-speakers of said dialect. For example, ebonics isn't a dialect; it's slang. It uses the same words from the English language for different purposes.
If I'm not mistaken, I always thought that there was an actual different dialect in Wales, but I could be wrong. Of course they speak English with a Welsh accent, but didn't they have an old Welsh dialect as well?
Also, it should be noted that dialects and languages are different as well. The only thing keeping a dialect from becoming a pure language is lack of grammatical structure. Every region in Italy has its own dialect, but they aren't languages. However, where I live they speak two languages: Italian and Friulano. Friulano is like a cross between Italian, English, and Latin. It's a barbarian language that's older than Italian which was brought here by the barbarians such as Attila the Hun. It's a sort of Celtic language with its own grammar structure and even literature. In Veneto, which is the region of Venice, they speak Veneto...which is a dialect. It's completely different and I understand almost nothing of what they say. It's like a completely different language, but without the proper grammar structure it's just a dialect.