Tie, bind both mean to make fast or secure.
They are often used interchangeably without marked loss, but since in both their primary and extended senses they carry fundamentally distinct connotations, greater precision in their use is often possible.
Tie basically implies the use of a cord or rope to attach one thing that may wander or move to another that is stable.
Bind , on the other hand, implies the use of a band or bond (see BOND ) to attach two or more things so that they are held firmly together or brought into union.
In extended use, especially when what is tied or bound is a person, both terms imply a deprivation of liberty and an imposed restraint.
Tie , however, specifically suggests a being held down by something stronger than oneself and an inability to get away or free oneself.
Bind , on the other hand, either suggests a being held together in a close union, for the sake of strength or mutual support or a being held down by such a bond, as a pledge, a compact, a duty, or an obligation, or by a bond of blood, marriage, or friendship.