Bungie said that there will be no menu. Some people have taken this as no start up menu and others no in-game menu (like the ones in Halo that would show you "Leave Game" and such). We have seen both a type of option/startup menu as well as an in-game inventory screen. I am going to assume that Bungie meant an in-game menu since there is no option for that on the PS4 and X1 controllers (no Start button anymore). I'm sure they will make it work.
This is not confirmation about the menu system. Everything is speculation. Destiny is still in its early stages so things will change and change again. Bungie makes the final call (but they like our good opinions).
The player editing/inventory doesn't count as a pause/in-game menu since the game continues.
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I think that picture kind of sums it up well, there will be menus, but they will be simplified, and your always in the world. There is no, let me leave the game to go to a competitive multiplayer menu or load up the campaign. There are still menus when necessary, but they will never take you entirely out of the Destiny Universe to do things. As far as start up goes, I don't know. Last years Need for speed on start up just dumped you into the world. So it may just dump you into your ship, or the last city when you start the game.