The word "like" has many meanings and uses.
Many are not part of formal writing, only of informal writing and oral language.
like - excludes
like = resembling, comparison, similar to
such as - includes
such as = for example, including, ...
I enjoy playing sports such as football and baseball. (= I enjoy playing footbal and baseball)
I enjoy playing sports like football and baseball (= I enjoy playing sports that are similar to football and baseball ... but not necessarily football and baseball!!)
Steve has recordings of many great saxophonists such as Ben Webster and Lee Konitz. Steve wants to be a great jazz saxophonist like Ben Webster and Lee Konitz.