We use Google apps for business for our emails and calendar. When one of my users (let's call him User A) sends an invite to another user (we'll call him User B), the invite is received as an email message and the message icon is also that of an email message.
When User A sends me a calendar invite I receive it as a calendar invite. It appears that only User B is affected by this problem so far. We use Microsoft Outlook 2010 with Google Apps Sync, for our emails.