Custom Tabs in Salesforce

Tab visibility can be managed from profile or permission sets. This knowledge article should answer your question. Org Wide Default settings is not to be confused with tab visibility, since it serves a different purpose mentioned at the end of this answer. I recommend you read through developer guides or trailhead modules to understand more about how object, record & tab is accessed in Salesforce. Following points should clarify your confusion about tab visibility. While creating a custom tabs, its visibility is not explicitly defined; so, it's basically available to be included in all the apps within the SF org. From App Manager, you could edit an app and include the custom object tab in it as well as define which profiles can access that app. This action restricts app visibility by profile and lists the custom tabs made available in an app. So, it doesn't explicitly restrict the tab visibility from app launcher or rather is not exclusively meant for controlling tab visibility. Tab visibility can be (and should be) defined at object level in profiles or permission sets, thereby making a custom object tab visible or hidden from an user, as shown in the table & ref screenshot below.

• PERMISSION SETS
  
• PROFILES
  
• DESCRIPTION
• Available
  
• Default Off
  

The tab doesn’t appear in an app’s navigation bar, but it is available in the App Launcher in Lightning Experience and on the All Tabs page in Salesforce Classic. Individual users can customize their display to make the tab visible in any app.

Available and Visible

Default On

The tab appears in an app’s navigation bar. The tab is also available in the App Launcher in Lightning Experience and on the All Tabs page in Salesforce Classic. Individual users can customize their display to hide the tab or make it visible in other apps.None Tab Hidden The tab isn’t available in the App Launcher or the All Tabs page, isn’t visible in any app navigation, and is excluded from API responses. I would recommend to read custom tab considerations as well.Org Wide Defaults' (OWD) purpose is to define the level of access to records that user doesn't own and is not meant for defining the visibility of the custom tabs. For additional sharing beyond the following OWD setting, you would have to use Role Hierarchy, Sharing Rules & Manual Sharing. Private: No Access to the object records that the user doesn't own or didn't create. Public Read Only: Only read access to all the object records that the user doesn't own or didn't create.Public Read Write: Both read & write access to all the object records that the user doesn't own or didn't create.