This command will cause an error
wc -l "~/tmp.txt"
wc: '~/tmp.txt': No such file or directory
While these command running fine
wc -l ~/tmp.txt
14 /home/user/tmp.txt
wc -l "/home/user/tmp.txt"
14 /home/user/tmp.txt
What is the difference? Can I do something to still include the "~" inside a double quote in case there are blank space in the path.
A tilde is only expanded if it's unquoted. Quoting (or, equivalent, prepending a backslash) disables expansion and turns them into literal tildes.
It's permissible to begin and end quotes mid-argument. You can quote the spaces while leaving the tilde unquoted. These are all equivalent:
wc -l ~/"file name with spaces.txt"
wc -l ~/'file name with spaces'.txt
wc -l ~/file\ name\ with\ spaces.txt