If Durant signs with anyone else this summer, that team won't get his Bird Rights, a mechanism that allows teams to go over the cap to retain players. According to NBA rules, players need to play at least three seasons with a team before the team can go over the cap to retain them for a full max deal. If a team other than the Thunder signs KD this summer, they still have something called a Non-Bird Right Exception they can use to retain players they've only had for one season, but it's not quite as appealing:
This exception allows a team to re-sign its own free agent to a salary starting at up to 120% of his salary in the previous season (not over the maximum salary, of course), 120% of the minimum salary, or the amount needed to tender a qualifying offer, whichever is greater. Raises are limited to 4.5% of the salary in the first year of the contract, and contracts are limited to four seasons when this exception is used.
It might not seem like much when we're talking percentages, but the totals add up over time. If Durant signed a one-and-one and then signed a five-year max next summer, he'd make over $235 million over the next six years. If he signed a one-and-one and then signed a four-year max using those Non-Bird Rights, he'd make a little over $168 million over the next five years. That's a $67 million difference, assuming the NBA's cap projections hold to form and don't shoot up more between now and 2017.