All of the blue icons on the world map those are all called "Jobs". Types of jobs include races, "missions", and deathmatches. Mission jobs can be anything that's not a race or deathmatch. Many of them, however, are "Last Team Standing" jobs which might as well be classified as deathmatch.
If you want a "mission" type job similar to the GTA single player missions, your best bet is to call Gerald.
Find Gerald in your contacts list and request a job. He will text you back with a job (this can take some time). Most of his jobs entail going somewhere, killing a bunch of people, stealing something, then delivering said something to him. That's as close to offline GTA as I've seen.