Ok. I'll take a shot. I've got more background in chemistry than metallurgy, but I'll do my best.
In general chemistry terms...
mass percentage is related to the weight of stuff and molar percentage is related to the amount of stuff. A "mole" is a certain amount of stuff (look up Avogadro's constant if you want to know more). It could be bushels or buckets or crap-loads of stuff, but suffice it to say we just use "moles" to keep everybody on the same page.
Take water ( H[SUB]2[/SUB]O ). Each molecule of water has 3 parts: 2 H's (hydrogen atoms) and 1 O (oxygen atom).
One mole of water also has 3 parts: 2 parts (moles) hydrogen and 1 part (mole) oxygen. So, the percentage of water made up by moles of hydrogen aka the molar percentage of hydrogen is 2 of 3 parts = 2/3 = 67%.
But the mass of water is ~18g per mole. The 2 parts hydrogen weigh about 1g per mole each, and the 1 part oxygen weighs about 16g per mole. So, the percentage of mass of water made up by hyrogens aka the mass percentage of hydrogen is 2g in 18g = 2/18 = 11%.
So with water, just like RX-79G said, the light element (hydrogen) makes up most of the number of molecules, but only a small part of the mass. And that's how one element could be a larger molar percentage, but a smaller mass percentage or vice versa.
Generally speaking, the composition of solids and liquids is usually described by mass or weight. It's not explicitly stated on the Crucible data sheets that I've looked at, but that is the convention, so I am guessing that the percentages of components you see in their steel data sheets are by mass. Based on that, it's my understanding that cpm s110v steel has 15.25% Cr, 9.0% V, and 3.0% Nb by mass, or 15.25% of the total mass of s110v steel is from the Cr.
Any differences in mass percentage values or conversions from molar percentage values might be due to rounding or computation in the app or chart you're working from.
As to how the differences would affect heat treat...
I'm not sure what the tolerances are... for example is 8.9999% V still s110v? what about 8.55%? etc etc. Different ratios of compounds will have different properties (edge holding, toughness, corrosion resistance, etc.), but the effects of changing the ratios might not be that straightforward. It's just like cooking. For some things, a little more or less salt won't make a difference, but for others... disaster.
How the ingredients combine also depends on how and when they're added, how they're heated, how they're mixed, etc etc. I don't know enough about steel manufacturing to know if say 1% more Nb in a given steel with a given heat treat will affect toughness, for example, but somebody around here does, I'm sure.
Hope that was helpful!
