What is the difference between using Form Submission Rule and Trigger Nurture for sending out a confirmation mail?

It depends on your needs. 

Adding a prospect to a nurture offers more info and possibilities (resend the email if not opened etc), but there is a 10-15 min delay between the form submission and the first email sent by a nurture. 

An autoresponder goes out immediately, but you can't trigger a resend AFAIK. 

So if reaction time is key, use an autoresponder. This does not prevent you from also adding the contact to a nurture, you just wont be able to create conditions on the autoresponder (opened, clicked). 

Hope this helps!

To add to what Damien is saying, I'd like to add an example of a situation. Let's say you created a form promoting a webinar. If you would just like to send one email for those who have filled out the form confirming their sign up and give them a link to the webinar, then you would want to choose the autoresponder, trigger email. If you would like to send them an email about the event, a day of reminder email, and a follow up email with the recording of the webinar only if their status for attending the event was yes, then you would want to use a trigger nurture. It really depends on how in depth you would like your communications with the recipients to be. 

To add to what Damien is saying, I'd like to add an example of a situation. Let's say you created a form promoting a webinar. If you would just like to send one email for those who have filled out the form confirming their sign up and give them a link to the webinar, then you would want to choose the autoresponder, trigger email. If you would like to send them an email about the event, a day of reminder email, and a follow up email with the recording of the webinar only if their status for attending the event was yes, then you would want to use a trigger nurture. It really depends on how in depth you would like your communications with the recipients to be. 

Absolutely. 

And if it's a support request, you definitely want to send a confirmation email right away to reassure the contact that the submission worked. 

It would be great if the delay for nurtures could be reduced.