I would not agonize over the specific white too much. If you are happy with the white from the Tile Shop, I would go with that. What color of contrasting grout are you considering?

I'm not sure, that was probably going to be my next question. We're going for a look something like this one but I have no idea what color grout this is. Any suggestions?

It does matter which white. Some have a slight cast of color that you might not want. This happened to me. After the white tiles were installed, they gave off a greyosh cast. I had them removed because they looked terrible!
The most popular look is what you are doing. Matching the tile to the cabinet color. I would suggest getting advise from a tile showroom, but you can't do this since you are ordering online.
My advise is to not rush this step. You will have extra tiles. Make up a sample board and grout it to make sure you like the look. Look at some of enduring's posts. She is tiling herself and she posted all her possible grout colors before committing.
I wound up with a cream crackle with the grout matching exactly to the tile. Since you are going very white, I like the idea of a contrasting grout to take away fromm the starkness. I like your inspiration picture.

Julize, I got my Lansdale Carrara at The Tile Shop. I used a contrasting grout from there too. I mixed their Natural with their standard white, 3parts natural:1part standard white. It took several samples and review help with family, sales staff, and GW to help me with the direction I wanted to go. It was funny, there was never a clear sample favorite with people. It isn't so much what everyone likes, rather it seems to be the discussion taking place to help you come to your own choice in the matter.

The grout I came up with looks the color of my stainless steel fixtures & appliances. Using straight Natural would have worked too I'm sure. The link I supplied shows wet grout, it lightened up quite a bit from my sample board.

Here is a link that might be useful: Samples of grouted herringbone backsplash, please give feedback

We used Delorean Gray grout with a very white tile for a look that's a lot like your inspiration photo; I second other suggestions to make a sample board, though. You can buy the color-matched caulk and run it between the test tiles instead of grout (much, much easier than mixing grout just for the sample board!) and get a pretty close approximation. Which white does matter, but at the same time it's incredibly difficult to figure out what the overall "feel" of the tile will be once it's up in an entire room, even with a sample board. Ours turned out fine, but is definitely a lot more white than I'd expected once there was a lot of it running up the wall. At the end of the day, though, as long as you're in the ballpark on color tones, it will work itself out.

Wow! I have been deciding the same thing for our kitchen. I think the color white does make a difference. Home Depot, Lowes, the Tile Shop, etc... are really different colors even though they're all white subway. Our kitchen cabinets are a crisp white (snowfall white from BM). I've ruled out The Tile Shop's white subway. It is the most white of all the subway samples I have. It matches our cabinets when it's on the wall in the shadow. I decided I don't want to match so I am going with Lowe's version of white subway. It is warmer and a slightly darker white than my cabinets. I asked a designer on houzz.com and she said they should NOT match. She called it layering whites and said it adds more depth and interest, and breaks up the whites. I am also going with a medium colored grout. I've made several sample boards. Definitely do this. You can get a small container of tile adhesive from Lowes and they also sell dry wall in 4x4 feet pieces. Ask the Tile Shop for some grout samples or try some from Lowes. You can just mix it with a little water in a cup and spread it on, let it sit for a few minutes and wipe off the excess (very easy). I am either going with Desert Sand or Mobe Pearl from Tile Shop. I will try to post a picture later today. Hope that helps!

Agree they should not match and in any case they will never match because they're different materials, installed on different planes, different reflectance. It is much better to pick something perceptibly and intentionally different. The grout color will also seem to impact the overall shade of the tile since at a distance your eye "mixes" the two together. Are you sure you don't want to consider a very pale grey or green tile?