What is the difference between "so far" and "yet"?

I would like to know the difference between so far and yet.

I have not sent two invitations so far.

I have not sent two invitations yet.

• I have not sent two invitations yet.
• I have not sent two invitations so far.

The major difference is that yet is a Negative Polarity Item (NPI), while so far isn't.
The way you demonstrate that is to remove the not from both sentences:

• I have sent two invitations so far
  is still grammatical, but
• *I have sent two invitations yet
  isn't grammatical (hence the *), because an NPI can't occur without a negative to trigger it.

"yet" must be used with negative or interrogative negative sentences but "so far" is used with affirmative sentences.

Hasn't she completed her studies yet?
Mohan hasn't eaten dinner yet?
Many applications have been invited but a few has been submitted so far.