The major difference between the two reply options is that one will open your Google Calendar in a new window showing you a confirmation of your decision and the other option will notify you within the email.
Take a look at the image below. You'll notice that I've chosen to reply 'Yes' to the invitation by clicking on the first set of choices available. My 'Yes' reply was confirmed in the 'butter bar' at the top of the email.
The convenience of this option is that you can immediately archive the email, place it in to a label, or delete it (but we recommend archive) and continue managing your email messages. Note that you can always double check your calendar to see the event on the calendar.
Next, we'll explore the second set of options that you have when replying to a calendar invite from within an email. When you click on your reply with these options, a new calendar window will open up displaying all the details of the calendar event providing you the option to add additional guests (if available), set specific reminders, and change the event color just to name a few.