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"I'm a laywoman in physics and recently found myself pondering..."

Given that you articulated your query so clearly despite this self-assessment , we should all wait for the questions you ask when you are no longer a laywoman in physics.

$(0)$ I'll start off by saying that in my opinion, the first part of @knzhou's answer is correct. The reason you are having trouble drawing a line between what is a liquid and what is a gas is that there isn't one; Both are Fluid (things that can flow). This is the macroscopic consequence of the microscopic fact that the underlying constituents are chaotic.

There are several ways to see that the distinction between Liquid and Gas is an artificial one, but, in most cases, the distinction between Fluid and Solid is something that is very clearly defined (In terms of macroscopic, observable criteria). Below, I list the ones I can think of. I wouldn't be surprised if there are more :

$(1)$ Relevant variables and Equations of motion: All Fluids are characterized by flow. That is, at each point in the material, one can assign a material velocity $v$, which is interpreted as the velocity of flow of the material. Equations of motion for any fluids involve $v$, and local thermodynamic variables (density, pressure, temperature...).

eg. Navier Stokes equation will describe both liquids and gases. What will change between liquids and gases are the coefficients that enter the equation, eg, coefficients of viscosity etc. But the form of the equations remain the same. The difference between liquid and gas is therefore merely a quantitative one, seen from this point of view.

In contrast, the solid phase will be described by elastic deformations (as against flow). The form of the equations of motion of a solid will be qualitatively different from the equations of motion for a fluid.

$(2)$ Symmetries obeyed: Fluids obey continuous translation symmetry. In case of many fluids (eg., water), Condensation involves explicit breaking of this symmetry, as the fluid settles down into a crystal (called ice). The fact that ice is a crystal implies that it obeys discrete translation symmetry.

This is once again an example of a qualitative distinction between Solid and Fluid. Once again, there is no possibility of drawing any such qualitative difference between Liquid and Gas, because they both obey identical symmetries.

Edit : I should add (and I know very little about this) that not all liquids freeze (ie. , settle down into crystalline order) as they condense. An amorphous solid (like Glass) is not crystalline, therefore solid glass has the same symmetries as molten glass ; Therefore, even though it appears solid, Glass is really a very viscous fluid.

$(3)$ The Phase diagram itself:

I'll refer to @knzhou's link for the phase diagram for water. (https://commons.wikimedia.org/wiki/File:Phase_diagram_of_water_simplified.svg)

When water boils at $NTP$ there seems to be a phase change not withstanding the above facts ; eg., The density clearly has a discontinuous jump between the two. But should this imply that we are dealing with two separate phases?

I'll not answer this directly. Instead, I will draw your attention to two facts that can be seen from the phase diagram itself. It is true that there is a range of pressures for which, when we increase the temperature, we encounter a discontinuous jump in density. The points at which this jump occurs is an extended curve in the $T-P$ plane. But it is also a fact that this curve terminates, at the critical point.

This implies the following : pick one configuration of water molecules that you think looks gaseous, and another that looks liquid (These two configurations refer to two points on the phase-diagram). There exists a thermodynamic process that takes you between these configurations (ie, a curve on the $T-P$ plane joining the two points) during which you encounter no discontinuous jumps in density!

tl;dr: If two "States of Matter" are connected via a continuous change in thermodynamic parameters, obey the same symmetries, and are governed by the same equations of motion, they are really the same thing. They should not, in my humble opinion, be recognized as distinct "Phases" in any well defined, macroscopically observable manner.

This last remark is relevant for the original setting of your question ; we can conclude that:

In a general case, there is no way you will be able to tell a liquid apart from a gas from a snapshot of all the molecules at a given time.

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