Different people categorize the Bond songs in different ways. One person I know has broken them down by who sings them; not by the singers, but by the point of view. That is, songs sung by Bond, by the Bond girl, by the villain, etc. Other people want to categorize by musical genre; pop, rock, jazz, etc.
Ultimately, though, I think there are only two, or perhaps three, meaningful categories.
A Bond song is either an action song or a love song.
The action songs, I think, are what most people consider a “real” Bond song. Starting with the James Bond Theme, Bond music moves in a thrilling way. The first real Bond title song, Goldfinger, is clearly an action song, despite the female point of view. Live and Let Die was a breakthrough as the first “modern,” rock-inflected Bond song, and it was also clearly an action song.
From Russia With Love was the first love song-as-title song (Underneath the Mango Tree was also a love song, but most people consider it incidental music, and not a real “Bond song”). The great breakthrough love song, the love song equivalent of Live and Let Die, was obviously Nobody Does It Better. That song single-handedly shifted the tone of Bond songs from then on. Despite two strong action songs in the 1980s (A View to a Kill and The Living Daylights), the tone of Bond music was love song ever since Carly Simon did it better.
Now, here’s where I might add a third category: Mystery song.
GoldenEye strikes me as a mystery song. It is haunting, compelling, mysterious. The theme is almost “the enemy within,” and this is appropriate for a movie in which Bond is betrayed by a close friend. And the next mystery song is also in a movie with a betrayal theme: Die Another Day. Madonna’s song is almost impossible to categorize by Bond standards, it is haunting and bizarre. I hated it, and then I grew to love it. It’s daring and strange.
By contrast, Chris Cornell’s You Know My Name is a disappointment. It’s a standard action song with below-standard vocals. Not a bad song, just, eh.