How to take a train to Frankfurt Airport?

I have not really taken the train for long distances however I am gonna be flying out next month and would like to get some help. I have gotten the following schedules from the db.de website: Nürnberg Hbf- Frankfurt(Main)Hbf 22:02-00:11 ICE 520 Frankfurt Hbf (tief)- F-Flughafen Regiobf. 00:47-00:57 S 8 For... show more I have not really taken the train for long distances however I am gonna be flying out next month and would like to get some help. I have gotten the following schedules from the db.de website:

Nürnberg Hbf- Frankfurt(Main)Hbf 22:02-00:11 ICE 520

Frankfurt Hbf (tief)- F-Flughafen Regiobf. 00:47-00:57 S 8

For the second train after you get to Frankfurt HBF is that S bahn (I assume streetcar) going to take you to the Airport? On the website it doesnt say that but I did select the Terminal 1Frankfurt Airport as my final destination.
Or is the second train have the airport on its stop or route?
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