The three to send, to send off, and to send out are distinguished by their motion and direction (actually and metaphorically).
To send is simply the action of causing something to go somewhere.
To Send off is the action of causing something to go somewhere from where you are to somewhere else.
To Send out is the action of causing something to go away from you.
From those literal uses we derive our metaphorical or analogical use.
For example, "I sent out a newsletter", because I am issuing the letter away myself to others. Or "we sent off the letter yesterday", because of the motion from ourselves to the recipient.
Others which describe a similar motion are:
To send away: the action of sending something to somewhere you are not.
To send along: the action of sending something in a particular direction, or along a particular path.
To send forth: the action of sending something toward somewhere
(edited to fix markdown)