The difference is that your master account name is what you use to login to the server so that you can access your characters and begin roleplaying with them in-game.
Your master account name is also what you may use to login to the user control panel on redcountyrp.com so that you can change your account's password, email, donate to the server if you so please, create new characters, or view details of your character in general such as age, phone numbers, addresses, economy, owned vehicles, and other things.
Your character name is simply the name of your character and you cannot log into the server with just that, it'll need to be your MA name.
To start playing you'll need to register on the main website (redcountyrp.com) and create your first character. You will need to pass a small quiz and it'll need to be reviewed by an administrator before you can login (using your master account name). Once done, you'll be greeted in-game by a small tutorial and you can start roleplaying.
Hope this explains what you were asking, and if not feel free to reply again and I can help you out!
Your Master Account is one account that houses all your characters and their assets, aswell as other assets that belong to you (donator levels, ts channel, ...), it's name you can chose upon registering (= MA name).
One MA can have up to four characters, which you can then name to your wishes (must be an RP name).