Tie someone down vs Tie someone up

tie someone down—restrict smb.’s freedom; encumber a person:

• I don’t want to tie you down, but you do have responsibilities here at home.

tie someone up—

1. bind a person with rope, string, etc.:

• The thieves left the old man tied up in the bedroom.

2. keep a person very busy:

• Writing this article should not tie me up for more than a week or two.

Note: The expression does not correlate in meaning with the phrase tie someone up in knots—make a person very nervous or worried:

• Kerry tied him up in knots just quoting his past utterances where he contradicted himself.