"Enter" is the catch-all term for all of these. You can "go into" or "come into" the store, or you can "enter" the store. "Come into" sounds a little odd, but it works. To my ear, if you said that you "Came into the store", I would expect you to give me more information (i.e. ok... and then what happened?). Some more colloquial uses where "Enter" would not work: 1. "Get into" - This can be used to mean that you started talking about something OR got interested in something at length. For example: "I didn't really want to get into a debate about cats versus dogs, so I walked away." I guess you could use "enter" here, but it would sound weird. Another example: "I recently got into this new TV show!" This means that you started to really become interested in it. You could NOT use "enter" here. 2. "Come into" - This could mean that you recently became acquainted with something, with a denotation that it was unintentional. For example: "I recently came into some money!" [Because I won the lottery, or because my inheritance finally stared to pay]. You could not use "enter" here.

There are many times where we often use enter, but could also use ¨go into¨, such as ¨He entered the building¨ or ¨They entered Colombia.¨ Sometimes we use entered for things that mean more like joined-- ¨He entered the race.¨ ¨She entered the program.¨ You might see a sign that says ¨Enter here.¨ (Although more commonly it would just say ¨Entrance.¨ )