Just as with paints brands, colored pencil names and colors will vary from brand to brand. Light blue from one company may well be a totally different color than light blue from another company.Just how light is light blue? How deep is deep red? Color ranges will be similar but each brand will have its own distinct hues and colors it chooses to put into a pencil.
Unsurprising this also can apply to white. In truth, white is not an absolute color, but will have qualities all its own. It can be bright, warm, cool, flat, shinny. Titanium white is not the same white as flake white or zinc white.
So working with white pencils will be the same. Each brand will have its own white. And each brand and line of pencils will have its own qualities. There will be other differences too. Coverage, how transparent or opaque that pencil is. How hard or soft the "lead". And some brands will lean toward the warm (yellow) or cool (blue) tone. Even many of the grays will appear when viewed alone to be just about white. Only when compared and used next to the most opaque white will you see the qualities of the grays.
Many manufacturers have a range of gray. They can run from 10% warm to 90% cool. Other brands will have names but the numbers will indicate that they are different colors.
This is very good when dealing with white objects. Working with several white and a full range of grays will help to contour and object. Even if the viewer cannot detect where one pencil starts and another leaves off, she will see the object, in this case the rose as having dimension.
Using different white also helps to alter and manipulate other colors. It is hard to shade from light to dark, but using layers of whites and grays helps you to move the pigments towards the effects you want.
The order you apply the pencil can make a difference. You get different colors if you layer pink then white than when you put white and top with pink.
How much also makes a difference. Two light layers will blend differently than a heavy layer. So a heavy layer of white with a light layer of pink will look different from a light white layer and a light pink layer.
You can also burnish layers with a harder white, like a Venus or Veri-thin pencil instead of the much softer standard prismacolor pencil.
You might find that although the prismacolor is nice and soft you might find it more useful to use the harder faber-castel white for adding highlights. And the Veri-thin make a much sharper line.
Each brand will react differently with mediums and solvents also.
Getting it right takes work and practice and experimentation. So we all need to take time to play with our colors. Get to know them and how well they play with others.