Just to add something to what the other members have already said: Yes, enter is more formal (and often less natural-sounding) than 'come in'. And remember that 'She entered the room' can be rephrased in two different ways : either 'She came into the room' or ''She went into the room' . The first is if the speaker/writer - or their point of view - is from inside the room, while the second is if they are outside the room.

Hi these phrases basically mean the same thing and can be interchanged. Here is a link that may help http://www.oxforddictionaries.com/definition/english/enter. However, it is more common to say come into the room or he came into the room than using enter and entered. This could be because it is considered more formal. For example, you wouldn't really say to someone, Hi Jane, please enter the room, it would be more normal to say, Hi Jane, please come in. You wouldn't really say, they entered the museum by the back door. instead They came in by the back door. So it isn't wrong just more natural to us come in or came in. Gillian

In your example they have the same meaning. i should add that the past tense of come is came, not camed.

"She came into the room" (notice the verb) and "she entered the room" mean the same thing, however "enter" is slightly more formal. It's a question of register. Also, "come into" can also mean "inherit" if the object is something of value, and not an enclosed space. "She came into a fortune when her great-grandmother passed away."

In your sentences and most of the time they have the same meaning, but not always. By the way, our first sentence should be 'She CAME into the room' here are 2 examples of when they do not have the same meaning I CAME INTO an inheritance AND I ENTERED a competition 'Enter' sounds a bit formal to me. I'd be more likely to say 'The President entered the room' rather than 'The president came into the room'