Language is the act of putting thoughts into words and then putting the words together to make a coherent word/phrase/sentence/story.
Speech is the motor act of speaking: turning the language that we have come up with in our brains into sounds, words and sentences that someone else can hear.
A speech disorder refers to a problem with sound production. For example, a child who says "wabbit" instead of "rabbit" almost always has a speech problem, but this will be determined based on their age.
A language disorder refers to a difficulty understanding or putting words together to communicate ideas. For example, a child who almost always says, "this one" when trying to name specific objects may have a language problem.