Inspiring and inspirational have similar meanings because they come from the same word. They refer to motivating something or someone either on purpose or without knowing it. The key difference between these two words is not the definition or meaning. They mean the same, but the key difference is their part of speech. Inspiring can be used as a main verb in a sentence, but it would need a helping verb to go along with it.
Inspirational is an adjective. It would modify a noun in a sentence. For instance, I would use inspirational to describe a teacher, so I would say that “Ms. Smith was an inspirational teacher.” Otherwise, I could say “Ms. Smith was inspiring her students to become whatever they wanted to be in life.”