James Bond is not a science fiction series. The villains may use space-age weaponry and Bond may use technologically advanced gadgets, but few would file the long-running spy series under sci-fi, particularly one where alternate timelines are concerned. And yet by virtue of its frequent reboots and where the producers have chosen to prize consistency over casting, there is a timeline of sorts to the Bond franchise. While the character remains young and has been played by different actors, there are points of consistency about how certain Bond films relate to each other even when the adventures themselves are largely standalone.
The Tracy Timeline
To understand how the George Lazenby, Roger Moore, and Timothy Dalton movies are connected, you have to look at one of the biggest incidents to ever affect James Bond personally: the death of his wife Tracy (Diana Rigg). While Lazenby does break the fourth wall and say "This never happened to the other fellow," at the beginning of On Her Majesty's Secret Service, he has mementos from the Sean Connery adventures, indicating that they're playing the same character. But this connection becomes cemented by the death of Tracy, an event that will come back in films led by Moore and Dalton.
While the Connery films never reference the death of Tracy, his connection precedes Lazenby, who finds objects from Dr. No, From Russia with Love, and Thunderball, indicating that it's the same character. At the end of On Her Majesty's Secret Service, Tracy and Bond get married, but Blofeld comes along and murders Tracy while trying to kill Bond.
At the beginning of For Your Eyes Only, we see Bond (Moore) visiting Tracy's grave. He then gets trapped in a remote control helicopter by a character strongly implied to be Blofeld (for legal reasons, the Bond producers could not officially use the Blofeld character in their movie). He gets his revenge by taking control of the helicopter and dropping Blofeld down a smokestack.
When we get to the much darker License to Kill, Bond attends the wedding of his friend Felix Leiter, but doesn't feel much like joining in the revelry. Leiter mentions to his new bride that Bond was married once, but his wife died. Tracy's death connects all these eras of Bond by giving him a personal loss in his past that's rarely touched upon, but surfaces for the Bond characters played by Lazenby, Moore, and Dalton.
The Brosnan Timeline
Everything resets with Brosnan as Bond. Not only is there a new M (Judi Dench) and Moneypenny (Samantha Bond), most importantly, Tracy is never mentioned. When we join Bond, it's clear he's been doing this for a while, but there's nothing concrete to connect him to any of the previous movies. For that matter, there's nothing much to connect the Brosnan Bond movies to each other, so they kind of standalone on this weird island where the biggest new addition they made to the franchise was having M played by a woman who had no patience for Bond's nonsense.
The Craig Timeline
This is where things can get a bit confusing. All of the roles are recast except for Judi Dench as M, so you'd be forgiven for thinking that Brosnan and Craig are playing the same character. However, Casino Royale, the first film featuring Craig as Bond, makes it very clear that Bond has just received his 00-status, meaning he's at the start of his career and recently received his license to kill. The Craig Bond can't be the Brosnan Bond because he's new at the gig even though M is the same character in both timelines.
But what about the name "James Bond"? What if that's just an alias and all of these movies are connected by a fake name they give to new agents? That's a good theory, but it gets blown up in Skyfall when Bond visits his childhood home and later sees the grave of his parents, Andrew Bond and Monique Delacroix-Bond. So James Bond is his real name (It's probably not the best idea to tell every person you meet that information, but that's tradition for you), and this James Bond is a particular guy separate from all the other Bonds that came before except for a minor Easter egg in No Time To Die that we won't discuss here because it's A) a bit of a spoiler, and B) it kind of throws everything into utter chaos.
Oh, and as for Never Say Never Again and Casino Royale (1967), don't even worry about those. They exist outside the official EON canon, and while they're fun to visit, they don't connect at all to any other Bond movie.