RStudio shows paths relative to what R considers the 'home' directory. On Windows, this can be specified by either the HOME or the R_USER environment variables. When these variables are unset (which they typically are), R asks the operating system what the 'personal' directory for a user is:
Which (from the Windows documentation) suggests that this is the Documents folder within the user's %USERPROFILE% directory:
https://msdn.microsoft.com/en-us/library/windows/desktop/bb762494(v=vs.85).aspx
So we're still actually showing a 'full' path -- we've just hidden the home directory bit inside the tilde.
Note that, after startup, R will populate the R_USER environment variable based on what folder it decided to use as the home directory.