No, they are two different devices. While retainers and mouth guards may look the same, they serve different purposes. Retainers are used to hold teeth in their new position after braces or other orthodontic treatments have been removed.
Mouth guards, on the other hand, are typically thicker than retainers and provide more cushioning. Mouthguards for sports are designed to absorb shock, whereas those for bruxism are designed to reduce the effects of teeth grinding.