Outlook Client and Outlook Web Access (.ICS File Format)

Hi, can anyone here please help to explain and provide some sort of supporting documents on my query.

Why is it when I receive a course/webminar booking through email (or maybe a travel reservation/schedule), I normally see the email through the Outlook Client (meaning it's visible and came into the inbox) but I could not find this same email in Outlook Web Access (even if I did a search in my email folders in OWA)? I believe the email is in .ICS format because when I open the email and I do a File\SaveAs, it auto default to an ICS file format. When I open the email, I can see that I can send it to myself (with the send button) and above got the message " You haven't sent this meeting invitation yet". Please note that the email received/booking is not in the form of an attachment. Whoever experience or saw this behaviour before, please help and assist. Thank you.