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Are there any rules or regulations as to when the term "based on a true story" or "real events" and so on can be used?

Does anything in the movie has to be somehow based on the real world, or is this phrase just a marketing tool and can be placed before any movie?

There are no rules as to when or how the term "Based on a true story/real events" can be used.

Sometimes it is a legit claim, but sometimes it is a pure marketing decision to fool the audience.

Basically you have 4 types of movies that make this claim:

1. 
   

   The fake true story

   
   
   
   • Movies claiming to be based on real events, but are not.
     
     Example: The Blair Witch Project
     
     The movie is presented as based on real events, but is actually fictionalized all the way through.
     
     There is no witch and no people died.
   
   


2. 
   

   The fictionalized true story

   
   
   
   • Only small elements are real, but the story around it is fake.
     
     Example: Enemy at the Gates
     
     The main character, the Soviet sniper Vasily Zaytsev, was a real person.
     
     But the movie shows a fictionalized version of him and most of the events shown in the movie never happened.
   
   


3. 
   

   The altered true story

   
   
   
   • These are movies are based on a true story, but small/large changes can be made to the story, timeline, actions, characters and certain events to produce a more thrilling story.
     
     Example: Argo.
     
     The history is real, but the involvement of the Canadian government and it's ambassador for example was much greater and far more important in real life than shown in the movie.
   
   


4. 
   

   The real true story

   
   
   
   • These are movies are based on a true story, where the only changes made are to be able to convert the story into a movie.
     
     Example: Apollo 13.
     
     The history is real, the events are real and the movie tries to stay as true as possible to that.
   
   

An additional case was mentioned by Steve-O in the comments (slightly paraphrased):

Movies that were "based on a true story" but where certain details were fictionalized because producers thought the actual facts were deemed too hard to believe by the audience.

This is actually a variation of the 3rd case: The altered true story.

The normal case is that, to make the movie more appealing, the true event is exaggerated.

But there exists a reversed version, where the true event is made less awesome.

An example of this case can be found in Public Enemies

The scene where John Dillinger escapes jail and takes 3 people hostage with a wooden gun is factually incorrect.

It was actually 17 to 33 people (depending the sources asked. Either the jail administrator or Dillinger himself).

However the director, Michael Mann, believed that this would be too unrealistic.

As mentioned in the comments Fargo is another prime example of the 1st case.

A movie that is advertised as "a true story", but was completely made up.

However this is a nice example for another reason.

The "true story" claim was so successfull that many people believed that the money from the movie was really buried somewhere.

Which lead to the urban legend around Takako Konishi, a Japanese woman who supposedly travelled to the USA and died of exposure to the extreme cold while looking for the buried money.

Because this in turn created a movie of case 3, the altered true story, called Kumiko the Treasure Hunter. Which tells her story, but is largely fictionalized.