"Trip" usually implies a destination (e.g., I'm going on a trip to Italy). "Journey", on the other hand, usually focuses on actually being on the road or in the midst of travel (e.g., his journey to Italy was long and difficult). You can also use journey for any kind of change in state or being (e.g., my inner journey to enlightenment). You would never say "my inner trip to enlightenment" -- "journey" is about the process of getting somewhere.
Shore and beach are very similar. In some cases, the shore means the actual place where the water and sand meet, whereas the beach means the entire place (sand, water, etc.). But they both can be used interchangeably -- when people talk about the Jersey Shore, they mean the beaches in New Jersey, so same thing.