It is generally assumed that the former ceremony predicts the latter. However, this isn't always the case. There are plenty of movies that won at the Oscars but not the Golden Globes.
The voting pool for each category is totally different. The Hollywood Foreign Press votes for the Golden Globes while The Academy of Motion Picture Arts and Sciences decides the Oscars winners. Because those voting for the latter are all industry members, the Academy Awards are generally considered more prestigious.
More often than not though, the HFPA and the Academy award the same films. However, there have been Oscars winners who went unrecognised by the HFPA. Here are some of the most famous examples.
'The Silence of the Lambs'
At the Golden Globes, 'The Silence of the Lams' earned only one out of its five nominations (Jodie Foster for Best Actress). This was rectified at the Oscars when the film won all five major awards of Best Picture, Best Director (Jonathon Demme), Best Actor, Best Actress and Best Screenplay (for Ted Tally).
'The Hurt Locker'
'The Hurt Locker' infamously won none of its three Golden Globe nominations in 2010. It went on to win six Oscars for Best Picture, Best Director (Kathryn Bigelow), Original Screenplay, Sound Editing, Sound Mixing and Film Editing. Ironically, Bigelow lost the Best Director and Best Drama Golden Globes to ex-husband James Cameron's 'Avatar'.
'The Godfather Part II'
Another film that won no Golden Globes was 'The Godfather Part II'. It lost all six of its nominations. However, at the Oscars, it was commended with six awards. These included Best Picture, Best Director (Francis Ford Coppola) and Best Actor in a Supporting Role (Robert De Niro).
'The Departed' and 'Braveheart'
Bet you never thought you'd never see these two films put together. However, they share in common that at the Golden Globes, both were only awarded for Best Director (Martin Scorsese and Mel Gibson, respectively). Both were the big winners at the Academy Awards, earning four and five Oscars in their respective years. Their awards included, of course, Best Picture.
'The King's Speech' and 'Spotlight'
In 2011, 'The Social Network' beat 'The King’s Speech' for Best Drama at the Globes. The reverse happened for the Oscars' Best Picture. Then in 2016, 'The Revenant' beat out Oscar winner 'Spotlight' for the Golden Globe for Best Drama.
In 2009, the Best Actor Golden Globes went to Mickey Rourke ('The Wrestler') and Colin Farrell ('In Bruges'). However, Sean Penn was awarded the Best Actor Academy Award gong for 'Milk'. The movie won for Best Screenplay and earned six other Oscar nods after getting only one nomination for Penn at the Golden Globes.
Other Best Actor awards
'Milk' isn't the only occasion where the Golden Globes differed totally from the Oscars in their Best Actor winners. Previously, Daniel Day-Lewis won the Oscar for 'My Left Foot' when the equivalent Golden Globe went to Tom Cruise for 'Born on the Fourth of July'. Denzel Washington lost the Best Actor - Drama Golden Globe to Russell Crowe ('A Beautiful Mind') but won the Oscar for 'Training Day'.
An earlier example is Charlton Heston, who won the Best Actor Oscar for 'Ben-Hur'. At the Golden Globes, he lost the award to Anthony Franciosa for 'Career'.
Best Actor in a Supporting Role awards
There have been a LOT of differences between the winners in the Best Supporting Actor category. In 1998, Robin Williams won the Oscar for 'Good Will Hunting' while Burt Reynolds won the Golden Globe for 'Boogie Nights'. In 1991, Joe Pesci won the Oscar for 'Goodfellas' (its one and only Oscar, shamefully). Prior to this, Bruce Davison got the Golden Globe for 'Longtime Companion'.
You may also be surprised to hear that Christoper Walken lost the Golden Globe for 'The Deer Hunter' to John Hurt in 'Midnight Express'. Walken did, however, win the Oscar. It was one of 'The Deer Hunter's five Oscar wins, including Best Picture, after it only won for Best Director (Michael Cimino) at the Golden Globes.
It's quite possibly the least popular Best Picture winner ever, but 'Crash' ought to be mentioned. After 'Brokeback Mountain' came out on top of the Golden Globes, the public were shocked when 'Crash', having won no Golden Globes (and a couple of nominations for Best Supporting Actor for Matt Dillon and Best Screenplay only), won three Oscars including Best Picture.