I think a big difference is: all of the English football team names implicitly or explicitly end with "Football Club." That is, the full name of "Manchester United" is actually "Manchester United Football Club" (sometimes "Manchester United F.C.").
There is no equivalent for American team names. "The Cincinnati Reds" are not "The Cincinnati Reds Baseball Club". It's just "The Cincinnati Reds".
If there is ever a need to disambiguate Liverpool (the place) from Liverpool (the team), you could say "Liverpool football club". If there were ever a need to verbally disambiguate between giant people living in San Francisco, and San Francisco Giants (a baseball team), we would tack on "The" - "The San Francisco Giants." If you needed extra disambiguation, you might tack on "... the baseball team", but it wouldn't really be a part of the team's name.
For the curious, here's a list of some American Baseball team names along with a list of some UK Football Club team names:
The New York Yankees, The Philadelphia Phillies, The Boston Red Sox, The Los Angeles Angels of Anaheim, The Chicago White Sox, The Chicago Cubs, The New York Mets, The San Francisco Giants, The Minnesota Twins, The Detroit Tigers, The St. Louis Cardinals, The Los Angeles Dodgers, The Texas Rangers, The Colorado Rockies, The Atlanta Braves, The Seattle Mariners, The Milwaukee Brewers, The Baltimore Orioles, The Cincinnati Reds, The Houston Astros, The Oakland Athletics, The Washington Nationals, The Toronto Blue Jays, The Miami Marlins, The Arizona Diamondbacks, The Cleveland Indians, The San Diego Padres, The Pittsburgh Pirates, The Tampa Bay Rays, The Kansas City Royals
Arsenal (the Gunners), Aston Villa (The Villa), Chelsea (The Blues, Pensioners?), Everton (The Toffees), Fulham (The Cottagers), Liverpool (The Reds?), Manchester City (also The Blues), Manchester United (the Red Devils), Newcastle United (the Magpies), Norwich City (the Canaries), Queens Park Rangers, Reading (the Royals), Sunderland (the Black Cats), Tottenham Hotspur (the Spurs), West Ham United (the Hammers), Wigan Athletic, Birmingham City, Blackpool (the Seasiders), Blackburn Rovers, Bolton Wanderers, Brighton and Hove Albion (the Seagulls), Bristol City, Burnley, Cardiff City (the Red dragons, used to be the Bluebirds), Charlton Athletic, Coventry City (the Sky Blues), Crystal Palace (the Eagles, used to be the Glaziers), Derby County (the Rams), Huddersfield Town, Hull City (the Tigers), Ipswich Town (the Tractor Boys) , Leeds United, Leicester City (the Foxes), Middlesbrough, Millwall, Nottingham Forest, Peterborough United (the Posh), Sheffield Wednesday (the Owls), Watford (the Hornets), Wolverhampton Wanderers (the Wolves).
And a bit of citation from "The IT Crowd": http://www.youtube.com/watch?v=gWJIQm9qH-w