The less important one is the United States Open, offering $8m (£4.9m) in prize money and regarded as the toughest major championship of all, which is being held this year at Congressional Country Club in lush and verdant suburban Maryland.
The other is an informal foursome involving a couple of Democrats and a couple of Republicans, whose handicaps are guarded like state secrets, at one of those "undisclosed locations" of which Washington is so fond. On paper the stakes are low, maybe a few dollars on the side per hole won. In reality though, they run into the trillions.
For this is not your ordinary bunch of duffers. On the tee for the Democrats are the President and Vice President of the United States, while the opposing pairing consists of John Boehner, Speaker of the House and the most powerful Republican in the land, and Mr Boehner's good friend John Kasich, governor of Ohio and a highly esteemed former chairman of the House Budget Committee.
That last attribute is anything but co-incidental. As the whole world knows, there is utter and hopeless deadlock here over how to tackle the budget deficit and reduce the national debt, currently $14trn and rising by over a trillion a year.
Commissions of the great and good have failed to come up with an answer: so has a bi-partisan Gang of Six senators on Capitol Hill. Making matters even worse, elections approach. In desperation, therefore, President Barack Obama is reaching for political Washington's most traditional lubricant, and the pastime of presidents par excellence: a game of golf.
These days it's not something to advertise. Ever since the disgraced former lobbyist Jack Abramoff was caught a few years ago taking elected servants of the people on all expenses-paid trips to sample the Old Course at St Andrews, the notion of politicians in golf carts has a less than wholesome ring. George W Bush, a keen golfer, at one point even claimed to have given up the game, anxious not to be seen indulging in so frivolous a pastime while American boys were dying in Iraq.
But the truth is they all do it – congressmen, lobbyists and, above all, presidents – and they've been doing it for generations. Indeed Congressional, on whose fearsome Blue Course the world's finest golfers are currently doing battle, was set up with five living presidents among its first permanent members, expressly for that purpose.
To quote from its original prospectus: "The member of Congress, brain cleared by the bracing air, and exhilarated by the play in which he is engaged, finds a more adequate conception of his problems of government; and from his contact with minds that know the nation's needs, develops more surely the solutions essential for America's wellbeing."
As a justification for schmoozing, that's as perfect now as it was 90 years ago. Not for nothing do they speak of "country club Republicans". In this age of Sarah Palin and the Tea Party, the breed is supposedly almost extinct, but far from it. The best golfer among today's political foursome is almost certainly the sleek and ever-tanned Mr Boehner, country club Republican in spirit, his skills honed by countless rounds with lobbyists and political cronies.
For presidents however, the game is even more precious: a momentary escape from the most crushing job on the planet, an activity where they're not shadowed by tiresome reporters, and a reminder of life's deepest verities. Crises come and go, friends can be as unreliable as enemies. But a slice or a hook is eternal, and no challenge as terrifying as a 3ft putt with victory on the line.
Almost every president has played golf; during the last century the only three that didn't were Herbert Hoover (even though he was among the founders of Congressional), Harry Truman (whose game was poker) and that killjoy Jimmy Carter. And the game has proved a most revealing gauge of character.
Dwight Eisenhower's enduring image as semi-detached and out-of-touch was sealed by his record of playing 100 rounds a year while supposedly running the free world. Anxious to avoid similar stigma, his successor, JFK, kept his trips to the course secret, even though he is reckoned the best presidential golfer of the lot.
Bill Clinton, another avid golfer and famously late for every appointment, was fond of "mulligans", bad shots taken again without penalty, and his habit of bending the sacred rules of the Royal and Ancient Golf Club. Sound familiar? Ditto Richard Nixon, who not only used to cheat, but was terrible with short putts. And if there was always something a bit frenetic about George Bush Snr, that is explained by his tendency to whiz round a course in a couple of hours, playing a game known as "cart polo" or "goofy golf".
Ronald Reagan's golfing days were mostly over by the time he reached the Oval Office, but he still played a traditional New Year's Eve round with cronies in California. Few presidents were worse at golf than Lyndon Johnson – but lousy outings at Congressional and elsewhere were more than worth it if you could arm-twist your partner into promising to vote for the Civil Rights Act. And, in any case, Johnson not only used mulligans by the dozen every round. He also reminded partners of one cardinal rule: "If you want to be in politics, you never get out on a golf course and beat your president."
Which brings us back to today's contest involving Mr Obama and Mr Boehner. The 44th President is not a natural schmoozer, but he doesn't lack cool on the course or off it, superintending the operation to kill Osama bin Laden on Sunday 1 May with the same nerveless assurance he had displayed a few hours earlier in his bunker shots, according to a congressman who golfed with him that day.
But that congressman was an admiring Democrat. Mr Boehner is not only reckoned to be 15 or so shots a round better than Mr Obama; he's also a Republican – so will he still let his President win? On such considerations may a US budget deal ultimately hinge. Who cares about that other small tournament under way at Congressional.
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