Yes, the grid still exists, and there are still different types of shaking grass. That's why there are only a few optimum places in Gen VI to chain because most patches of grass are either not big enough or have too many holes in them.
The differences are:
- you can step outside of your patch of grass in order to run around and go back in to use the radar again; as long as you don't leave the route/ area, your chain will continue (as indicated by the music playing)
- the optimum grass for you to go into is 4 steps or more away. In Gen IV, it was 4 and only 4 steps away
- the optimum grass is also not shaking next to another patch of shaking grass
- any grass that shakes near the boarder areas (not of a 4x4 grid but the actual line where there is physically no more grass to go into) is liable to end your chain when you come out of it
- while in Gen IV you had to remember the type of shaking grass you first went into and go into the same shaking grass, in Gen VI you only need to look for fast shaking grass (there's medium and slow as well). That will hold the Pokemon that you need.
This video by Pokeman Academy will teach you pretty much everything you need to know about shiny chaining.