Scenario 1: Not receiving calendar invitations to your Gmail inbox from Apple Calendar users.
Scenario 2: You can send invites from your Google Calendar, but if you send from your calendar app, the invites don’t go through.
Your primary email address (be it Gmail/Outlook/Yahoo) is registered as your Apple ID. Your primary calendar is not your iCloud calendar, which is linked to your Apple ID Email address.
Solution (that worked for me)
Edit the calendar preference settings while logged into Apple iCloud. Be sure to login to icloud.com on your desktop/laptop.
Thank you to this answer on Stack Exchange for helping to find the solution to the problem.
Here is a quick video tutorial to help you edit the Apple iCloud Calendar invitation settings.