Buying back shares reduces the actual portion of the company that is being traded on the secondary market. Splitting the shares just changes the overall number of shares (and what portion of the company they represent) that are available to trade.

Buy backs reduce the supply of shares available for trading, which generally causes the price to rise as demand stays about the same. Share splits do not affect the supply/demand of shares, it just changes the nominal unit of measure for trading, and does not affect the actual value of the company or your investment.

So overall, no, they're not really counter intuitive actions. Doing a buyback can boost value for shareholders, followed by a split, which reduces the per-share price to help keep the price at an attractive level to potential investors.

That's not always the case. It probably is one of the primary reasons why Apple announced their buyback. They're reducing their cash on hand to prevent paying an accumulated earnings tax. Other companies, it may not be so much of a factor.

A lot of board members and chief executives are paid in stock and stock options. A share buyback when the company is doing well can help to boost their total compensation while also adding value and building confidence for investors. It can be a win-win for all parties involved.