There is quite a confusion among English natives when it comes to the appropiate definition of each term. So let's state this concepts before it gets started:

-Padel: a sport played by 2 or 4 people (usually four) in a court smaller than the tennis one, surrounded by walls and glass, with a net in the middle. Players use a special tool called paddles.
Below you have a sample picture.



-Paddle: the actual tool players use to hit the ball. It's something between a table tennis bat and a tennis racquet. The weight of it ranges from 340 to 400 gr. and the usual center width is 38 mm. There are several shapes, materials and designs, each one with its own features. Some people call it paddle racquet, others padel racquet.




-Paddle tennis: a variation from traditional tennis. Played in a small tennis court, it lacks the padel walls but is played with paddles. In the end, it could be summed up as a mixture of padel and tennis.



Though padel and paddle are pronounced in a similar fashion in English, there isn't this confusion in Spanish. So, if you ever happen to look for paddles in Spanish, search "palas de padel".
Well, I hope this hints can finally solve this huge confusion.