These two functions take very similar parameters and allow you to add or remove an email address to / from a group. Email addresses in groups allow you to track activity and filter mailings. Groups are not the same as lists, however. For more about groups, see this knowledge base article.
The two calls are very similar:
All the parameters are required. The <email> parameter must be a single email, and the <groupid> an existing group in your account. The simple API does not check for the email address’ existence in the specified group; as such each invocation is idempotent (can be called repeatedly with no ill effects). In other words, if adding to a group and the address is already in the group, nothing changes. Similarly, if deleting from a group and the address does not exist in the group, nothing changes.
The calls return XML indicating success or failure. Group IDs are available from the UI, or via the REST API. These calls only affect existing groups, and cannot be used to create or delete groups, nor do they operate on the Suppression Lists.