There is no difference between ~ and ~/ they are both the same: shorthand for "the current user's home directory as defined in /etc/passwd".
~username is shorthand for "username's home directory as defined in /etc/passwd"
Now, it sounds like you installed FreeBSD with a single large / partition for everything (or without a separate partition for /home). Which means the default home directories for all users is /usr/home/, and "/home" is just a symbolic link to it, as a lot of software expects "user homes directories" to be under /home.
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