“ls $PWD” and “ls .” get different files, strange caching perhaps

In most shells including bash, pwd is a shell builtin:

$ type -a pwd
pwd is a shell builtin
pwd is /bin/pwd

If you use /bin/pwd, you must use the -L option to get the same result as builtin pwd:

$ ln -s . test
$ cd test && pwd
/home/cuonglm/test
$ /bin/pwd
/home/cuonglm
$ /bin/pwd -L
/home/cuonglm/test

By default, /bin/pwd ignores symlinks and prints the actual directory.

From info pwd:

`-L'
`--logical'
     If the contents of the environment variable `PWD' provide an
     absolute name of the current directory with no `.' or `..'
     components, but possibly with symbolic links, then output those
     contents.  Otherwise, fall back to default `-P' handling.

`-P'
`--physical'
     Print a fully resolved name for the current directory.  That is,
     all components of the printed name will be actual directory
     names--none will be symbolic links.

The built-in pwd includes symlink by default, except that -P option is used, or -o physical set builtin is enabled.

From man bash:

pwd [-LP]
              Print the absolute pathname of the  current  working  directory.
              The pathname printed contains no symbolic links if the -P option
              is supplied or the -o physical option to the set builtin command
              is  enabled.  If the -L option is used, the pathname printed may
              contain symbolic links.  The return status is 0 unless an  error
              occurs  while  reading  the  name of the current directory or an
              invalid option is supplied.

. is not a bash (or any other shell) built-in. Each and every directory has entries . and .. in it. You can verify by cd'ing to some arbitrary directory and doing ls -lia . You will see . and .. entries. I had you use the '-i' flag on ls to get inode numbers: note them for . and ... Go up a directory, but doing cd .. or cd /something/soemthingelse/whatever. Do ls -lia again. Notice that the inode number of . is identical to that of .. in your first listing. Every directory has directories in it when created, named "." and "..". The "." entry has the same inode number as the directory's name does in its parent directory. The ".." entry is always the parent directory. If you do ls -li / you will see that "." and ".." have the same value.

This convention eliminates the need for special case code to reference the current directory: it's always named ".". It eliminates the need for special case code to "go up one directory": it's always "..". The only special cases are the root directory, and network-mounted filesystems. The filesystem root has "." and ".." with the same inode number, not different. Network-mounted filesystems have a discontinuity in inode numbers at the mount point, and behavior depends on what the remote filesystem is, and what protocol is used to mount it.

As far as the change in prompt, when you invoked mv ../ttt ../tttt, you actually renamed your shell's working directory. You didn't invoke a shell command that checks working directory until you did cd ., so the intervening pwd reports the old name, /tmp/tt.