My user would like one group of users to be able to have only 'create' only access to a custom field set that will be in a contact's tab, and for another group to be able to have 'edit' access. I have tried this out and it doesn't seem to be possible using ACLs - at least not 'out of the box' (unless there's an extension that will help with this?). There's a message on the 'Manage ACLs' screen that says "NOTE: For Custom Data ACLs, the 'View' and 'Edit' operations currently do the same thing". This kind of requirement is perfectly reasonable and probably not unusual - but is it possible for contact custom data?
One way of doing this, if you were using Drupal, would be to use Views and Webforms. This is our 'go to' approach when needing to finesse who can see/do what.
I would use Contextual Filters to show the logged in users the data they should be able to access, and then use links to take that Contact ID over in to a webform_civicrm form for doing any editing.