What is the difference between a mural and street-art?
Generally a mural is any art which is applied directly to a wall, often a painting or drawing although the term can also be applied to sculptural reliefs. 

Street art is a bit more general and is usually used for art which takes place in public spaces. As well as semi-permanent media like murals this can also apply to performances or temporary media like pavement drawing. The term can also be applied to things like portrait drawing which take place on the street although in this sort of context the term 'street artist' might be more appropriate than street art. 

Historically graffiti generally implies casual drawing of painting on public or private structures often without permission. However it is also associated with a set of painting styles using aerosol cans, often on quite a large scale. As with all definitions of art what is and is not intended as 'art' is debatable and mutable. 

In many western cultures street art has associations with urban subcultures and political protest although again, it is becoming increasingly mainstream and there are a few examples, notably Banksy where it it pretty much part of teh mainstream elite art market...although again what this actually means is a whole other debate in itself. 

The actual style and medium can vary a lot. From the context of the question it seems like you are thinking mostly about images painted on walls etc but most cultural forms, dance, poetry, music, theatre ect  have some 'street' version which may be either more of less 'underground' or be part of more mainstream cultural as seasonal or festival events. 

Consider also Yarn Bombing and Guerrilla Gardening 

There is also some overlap with public art (typically large scale sculpture) although street art implies something less formal and less permanent. Similarly 'street' tends to imply a more urban setting.