It is a matter of completeness. Any time a public company is taken private, ALL outstanding shares owned by the public must be acquired. The procedure is complex but it must be done, generally, by public announcement and every public owner of the share must be paid if the acquisition is approved and goes ahead.
A share buy back can only be done by the company issuing the shares. It only involves a limited number of shares which is acquired in the open market (normally). Share buy backs need to be approved by the Board of Directors. (ie the representative of shareholders). It isn’t something the managers of the company can do without authorization.
This is a pretty superficial (technical) explanation. The reasoning and motivation behind either of these actions are varied.
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