These are known to be two different types of conditions. When you say dysarthria, this is a type of condition wherein a person may have some trouble with speech. When you say aphasia, this is related more to the language that a person may speak.
For example, when you say aphasia, you know for sure that this is a type of language disorder wherein the person cannot speak the language anymore because of a medical condition such as a stroke.
Some acquire this because of other types of brain injuries. With dysarthria, the speech may be slurred and will not be too clear.