So you have to pay to use Skype? I thought skype would act like FaceTime on Apple or Hangouts on Android!
Skype to Skype is free, Skype to phone number isn't.
So even if you have Skype on your phone and you are calling another Skype user who has it on a phone, it is free, you are calling using the Internet so effectively call over IP.
If you call the same phone from Skype but use the persons phone number, you are no longer calling over the Internet and are using some one else's telephony equipment and you need to pay.
So just make sure you don't call phone numbers.
PS If you do want to call phone numbers that is when you buy Skype credit, and to the OP it does look like you need the app as it is the only way to input a phone number, although if someone has texted or called you and they are in your phone book/contacts list maybe you can call them.
Just tested this, a new contact had sent me a text, so I can now call him from the messaging and Skype App and I suppose it will use Skype Credit although it actually just looks like a mobile call so maybe not.