It happens in Portuguese, Italian, Spanish, French,... saber = shows abilities, you have known about that, you understand the point. Conhecer = you know that for some or a long time before, like musics, people, places, etc, or if you have the knowledge about something. - você conhece essa música?, eles já cohecem a Maria, eles sabem cozinhar (they know howto cook)
You can associate "conhecer" to "recognize" (reconhecer). It's not the same meaning, but "everthing (that) you recognize, you know. (Tudo que você reconhece, você conhece). You can also think of it as "to be aquainted with".
And you can associate the verb "saber" to "know how" (o saber - noun).
Eu sei cozinhar (I know how to cook).
Eu sei matemática (I know math) - It's not about recognizing, but having knowledge.
Sometimes saber and conhecer get mixed up, and there are some cases where both can be used.