AWS Simple Storage Service is a single repository or a file where you can store all kinds of objects. There is no concept of folders in it, just a single file system. If you are non-technical, it is just like any Cloud Storage, (such as dropbox, onedrive).
AWS Storage Gateway, thus the name is gateway for reading and writing data between storage services. For example, AWS S3 to your on-premise system and vice versa.
To put it simply, S3 is the storage service and AWS Storage Gateway is the service which helps to upload data to S3.
You can check out this AWS S3 tutorial for more information. If you are trying to become AWS certified then check out this - AWS Certification.