2 Separate things with HHonors. Points and miles. Most traditional airline programs give out miles. Southwest Airlines, through their Rapid Rewards program, keeps track of ponts instead of miles. Once you have 16 SWA Rapid Rewards points, you get a voucher for a free round trip ticket on Southwest, along with a bunch of drink tickets.
If you select the option to double dip with Hilton Honors, you get your honors points for the stay and you get credit on the frequent flier program of your choice. If you choose Southwest, with each Hilton stay, you get 0.5 point. Marriott has a similar deal along with Hertz and Avis. You just have to make sure your reward program for Hilton or Marriott or Hertz has your Southwest Airlines Rapid Rewards number in your profile.
Now, if you have a Hilton Honors Amex, you get 5 Hilton Honors points for each dollar you spend at a Hilton property. They also give you 5 points per dollar if you pay your cell phone, cable bill and gas stations with your card. Everywhere else you get 3 points per dollar spent. These points get transferred to you Hilton Honors account once a month and can be used for merchandise, hotel stays and vacation packages. Most hotels are around 20,000 points per night, some are 10,000, some are 40,000.
I think you may be able to use your Honors points to get airline tickets too, but the honors points have nothing to do with the Southwest Airlines Rapid Rewards points. Hopefully that answers your question.
Looking at the Hilton Honors website, you can
exchange 10,000 honors points for 1 Southwest Rapid Rewards point. That means for 160,000 honors points will get you 16 SWA points and a free roundtrip ticket. (Doesn't seem like much of a deal to me) Go here for more airline ticket details:
hiltonhhonors.com/airline