They are waterstones but they use ceramic abrasives. The Shapton is Splash-n-go while the Bester/Beston is a soaker and will need about 30 minutes in water before it will work correctly.
Although you have selected good stones I don't know why you would pick those two to use in a progression. The Shapton Glass DO NOT PLAY WELL WITH OTHERS, sure, you can mix and match all you want but your results WILL suffer. Every waterstone is unique and my #1 rule in making a set is to always stick to one brand or line of stones. This way you stay consistent with abrasive, feedback, and abrasive size. Speaking of abrasive size, please realize that the numbers you see on waterstones are not universal, just because it says "4000 grit" does not mean it will act like everyother stone in that grit range. Binder, abrasive, abrasive content, stone hardness, rate of stone wear, mud production and type of mud can all play a part in how a waterstone interacts with a specific steel.
So, just because the numbers flow doesn't mean the stones will too.