The Visibility of a form is controlled by clicking the 
icon. This icon functions as a 3-way toggle. The icon tells you that your form is a private, meaning only you (the owner of the form) can edit, test or use it. Clicking this icon once will change it to this 
icon and make the form usable by anyone who has an account (username/password) and is logged in to your tenant. Clicking the icon again will change it to this 
icon and make the form public so anyone can use it even if they are not logged in. If the form is public, clicking the icon will make it private.
The visibility can also be changed directly in the form designer using the form visibility property as shown below. When Live Forms is embedded in another product such as Live Forms for Confluence embeds the form designer in Atlassian's Confluence wiki product, this method of setting visibility is the approach as you do not have access to the icons described above.
You can publish any form regardless of whether it is public or private, but if it is private, only the person who created it can edit it or test it. Another user may log in using your ID and password, however, so it is possible to collaborate on a form without sharing it, as long as two of you not editing the same form at the same time. Two or more people may test the form and view submissions at the same time.
Similarly, if a form is public in tenant, only users with accounts in the tenant will be able to access the form.
Until you make your form public all other users will see this error message when they try to access the form: "The requested resource is private. You must login as the owner to access it."
A form made public this way is accessible to anyone with the form's Url. There are other methods of sharing forms that have increasingly higher levels of security. See form security for details.
If you have made your form public and users have begun submitting it, you'll need to use caution when modifying your form. If users access it while you are editing it, they will see error messages indicating that the page is being refreshed or that the form is invalid.
You can mark your form private until you are done updating it, which will prevent new users from accessing the form, but if users happen to be completing the form when you switch it from public to private, they will see error messages. For Professional Edition users a better approach if feasible is to edit the form in a copy of your application running on a staging server. You can then replace the current form with the new form by removing the original application from the staging server and uploading the new application.