They are both commonly used ways of saying "Thank you." Teşekkürler literally translates to "Thanks" and teşekkür ederim translates to "I thank you." Less common is teşekkür ediyorum. That translates to "I am thanking you." It is more formal and is reserved for strong expressions of thanks, but can also be taken as smart alec.
Just a question outside of this, did anybody actually knew how to speak a whole language from this app? I love it but i don't want to just learn the basics from it