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Specific heat capacity refers to the heat capacity per mass. As you can probably imagine, it is not always useful to talk about the total heat capacity, e.g., if you want to characterize not an object, but a type of material. There is also molar heat capacity, which is the heat capacity per 1 mol particles and which is directly connected to the specific heat capacity through the molar mass of a material.

For specific impulse, it is about momentum change (which is force) per ejected unit of mass. So that isn't necessarily comparable to specific heat capacity because it does not just depend on the material that is ejected but rather by the exit velocity of the ejected material. In this case, you might also consider the volume-specific impulse, which gives you the force per ejected unit of volume, as you have limited space in a rocket.

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Forty__ gave a great answer. But just to add a more general conclusion. "Specific" usually means "per quantity of that thing." It doesn't necessarily need to be mass - although the two examples you gave are per mass. "Specific gravity" is a fancy word for density - or mass per volume.

And yeah its a horrible word. Doesn't make any sense with the normal English definition of specific. Old science terms are often bad science terms in modern English.

Specific gravity is the ratio of the density of something relative to that of water. So water has a specific gravity of 1, while something more dense than water has a specific gravity greater than 1. This also means that specific gravity is unitless, while density is not (e.g. kg*m^-3)

But agreed that "specific" usually means per something or relative to something.

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I think it means “per unit of x”, not mass specifically (excuse the pun). For example I sometimes have to report specific energy consumption for sites and that basically means MWh per unit of production or something like that (could be mass but not necessarily). It’s basically for benchmarking purposes

> And yeah its a horrible word. Doesn't make any sense with the normal English definition of specific. Old science terms are often bad science terms in modern English.

I'd guess it's a bit too literal translation from the German spezifisch which means "specific", "particular", but also "intrinsic", which is much closer to the actual meaning. (For a long time, German was the lingua franca of physics.)

Even though it may be technically wrong specific heat is often used to mean molar heat capacity even in many publications.

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"Specific" was, at least originally, a generic term to indicate that the parameter being discussed has been normalized by some relevant unit to turn it from an extensive property to an intensive property. Occasionally in the context of specific heat, you will actually see people write out "mass specific heat" or "volumetric specific heat" or "molar specific heat".

People working in a particular context almost certainly just use the term specific heat to refer to whichever specific intensive property is most often relevant, so it doesn't surprise me to hear that some people use it to mean molar specific heat rather than mass specific heat.