~ means the home directory of the registered user, while ~/ means the path to the beginning of the directory.
From here :
Tilde (~) is a shortcut for Linux to indicate the user's home directory. Thus, the tilde slash (~ /) is the beginning of the file path or directory under the user's home directory.
On a side note If you see ~Gowthaman/ , then this will be the Gowthaman user home directory
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