Choosing to save your playthrough when jumping into a chapter means if you continue on from that point, it will take your new choices into account. It will save the new options on your flowchart while showing your previous choices. If you choose to save the actions you do in a chapter and then jump to a future chapter, it will continue on from your first playthrough, since it's going off the data from the previous chapter. This means you can't just jump around killing Connor or killing Leo and then jumping forward to Waiting For Hank and read the report about android families.
You can also jump into a chapter and perform the actions required for a trophy / read a magazine and then quit to the menu. It will unlock the trophy / add the magazine to your collection, so you don't have to finish the chapter like I foolishly though for a bunch of my misc trophy unlocks.
The trophies that require longer playthroughs than jumping into a chapter then quitting are the magazine ones (some magazines change in chapters depending on actions taken in previous chapters), keeping everyone alive (starting with Simon in the Media Tower chapter. You have to keep Connor, Kara, Alice, Luthor Markus, North, Josh, Simon, and Jerry alive), and killing Connor the required amount of times (up to Hank's suicide, I believe. Mine unlocked after he shot himself and North declared war on the humans).
Hope this helps fellow trophy hunters and people wondering about jumping in chapters to view new things.