A noun is often used as an adjective to indicate something of that "type". For example, a "car part" is a part of type "car", that is, a part that is intended for use on a car.
A noun used as a possessive, of course, indicates that the thing "belongs" to that noun in some sense. A "car's part" is a part of that car.
Often the distinction between the two can be subtle. "I found a dog collar in the park" -- I found a collar of the sort that is worn by dogs. "I found a dog's collar in the park" -- I found a collar that belongs to a dog. In context they both mean pretty much the same thing.
But usually the possessive is more specific. We say, "This store sells car parts", that is, they sell parts for cars. We'd be unlikely to say, "This store sells car's parts", because that would sound like they sell parts for one particular car. But I'd say, "My car's steering wheel is loose" rather than "My car steering wheel is loose", because I'm talking about the steering wheel of one particular car.
In this case, it's common to say "the morning news" to refer to a TV news program that is broadcast in the mornings, or such programs in general. "This morning's news" means something that was in the news this morning, one particular morning.
"I heard about the hurricane in the morning news" -- I heard it on a news program that is broadcast in the morning. "I heard about the hurricane in this morning's news" -- I specifically heard it this morning. In context, the difference is very subtle.
But, "I like to listen to the morning news" -- I listen to it regularly. You wouldn't say, "I like to listen to this morning's news", because you really could only do that once.