I’m aware that there has been some criticism of the IPA’s classification of approximants, as well as debate over the merit of the term itself. However, my understanding is that approximants are the least constricted phones that are still consonantal in nature and can be classified as occurring at a particular place of primary articulation.
Because of this, many approximants sound extremely similar to the fricatives at the same place of articulation. Some approximants even use the same glyph as their corresponding fricative, like [ʁ̞] and [β̞]. In addition, [ʝ] sounds like a version of [j] with slightly more constriction and [ʋ] sounds pretty similar to [v].
However, this does not seem to be the case for the coronal approximants like [ɹ], the alveolar or postalveolar approximant, and [ɻ], the retroflex approximant. To my ears, these phones sound nothing like the corresponding fricatives [z], [ʒ], and [ʐ].
Why is this? Is there just more acoustic variation of coronal phones, or is there something fundamentally different about these particular approximants?