Aside from having an s3-compatible layer, that's where the similarities end. Minio is self-hosted, and doesn't provide the additional workflow processing, etc.
Minio is an awesome object storage solution with great features such as the S3 gateway but from what I know they don’t have a processing layer.
At Koyeb we also have an S3 compatible layer to let users send, process, and store (on any cloud or your own edge Minio) data. As @bdcravens said, its where similarities end, plus Koyeb is entirely managed.