Along with what Dev said but I'll explain a few different ways you can enter these types of chat since Dev only explained one of the ways:
If you want to whisper to your friends directly you can open your Friendslist and click their name. Then options will pop up and you can pick to whisper them from there as shown below:
Another way you can do it is by clicking that little box on the bottom left of your screen that says "local" and selecting "whisper". There will then be a bar where you can type in the person's username that you want to whisper. Once you enter a name you can then whisper that person.
Another way to whisper people is to just walk up to them and double click them. A box with their user info will pop up. Click "whisper" and you can send them a message.
As for Group chat if you are a part of a group just select the little box that says "local" on the bottom left and switch the chat to group to talk to just your group:
