Tongue placement is quite different. But the sound both produce is very similar. An important aspect of American r sound is that the tip of the tongue NEVER touches the tooth ridge during this sound!
Method 1 (solid): the back of tongue is raised so the sides of the tongue touch the back teeth. The center of the back of the tongue is lower and the air travels through this groove to create the sound. The tip of tongue may point upward, or may be left low.
Method 2 (dashed): The tip of tongue is raised and curled back behind the tooth ridge while the back of the tongue stays low.
Also, the r sound interacts with adjacent sounds, which can result in positions that are a combination of the above methods.