It's easy to use the terms "mass" and "weight" interchangeably in casual conversation, but they don't refer to the same concepts at all.
We only swap them out so freely because we're so used to discussing these matters here on Earth. However, as we continue to send things into space, be it cargo for the International Space Station, Tesla Roadsters or, eventually, maybe, colonies to Mars, we need to start appreciating that mass and weight are measures of two different things.
A weighty or massive problem
The difference between mass and weight, at its most fundamental level, is contextual. Weight is something that will change, depending on your location in the universe, while mass is the amount of matter in a body, and this doesn't change depending on where you are, barring the addition or subtraction of matter or energy.
That was probably as clear as mud. Let me explain.
Weight changes because it's not actually a measure of you but rather a measure of the downward force gravity exerts on you. This is why you weigh less on the moon than you do on Earth, weigh more on Jupiter and weigh nothing in space. The gravitational pull of these areas is simply different, and that changes your weight. While we talk about weight in pounds (lb) or kilograms (kg), it should be measured in newtons (N), the standard unit for force.
Mass, on the other hand, is constant and is the sum total of all the matter that makes up a body. An object has the same mass wherever it is, regardless of the local gravity. Mass is represented in kilograms, which can in turn be converted to units like pounds, ounces, stones, etc.
(Some of you may be about to argue with us about pounds also being a measurement of force as well as a measurement of mass, but this is officially incorrect. Yes, pounds can be used as a measurement of force, but the U.S. National Institute of Standards and Technology identifies the pound as a measurement of mass, and we're not going to argue with them. Please direct your frustrated emails, Facebook messages and tweets to Walter Copan, the current Under Secretary of Commerce for Standards and Technology who heads up the NIST.)
To determine something's weight, at least on here on Earth, it's a simple mathematical expression: W = mg. W is weight, m is mass and g is the local gravitational force. Here on Earth, g is 9.8 newtons. Simply multiple something's mass in kilograms by 9.8 and you have its weight.
So, for example, the average American male, per data collected by the Centers for Disease Control (CDC) between 2011 and 2014, has a mass/"weight" of almost 196 pounds. That converts to 89 kilograms. So 89 times 9.8 and you get 792 newtons, the average actual weight of an American male.
Incidentally, an electronic bathroom scale gives your "weight" by measuring the force exerted on a pressure sensor. The more force exerted (meaning the more mass you have), the more of an electric current is generated. The current is measured and converted to a unit that represents your mass/"weight." That's what appears on the display before you step off the scale.
Amassing the mass in space
Now, no one's going to correct you about this when you say you weigh however many pounds you weigh instead of using newtons. All objects on Earth have both a weight and a mass, and the measurement of one is almost exactly proportional to the other, so using them interchangeably on this planet is fine in every day conversation.
As we go into space, however, mass, not weight, becomes far more important. Packing things onto a space ship is an issue of mass because the item's weight will change depending on where it is. Crates of habitat complexes for a Martian colony are going to have a different weight when they launch from Earth than when they ultimately land on Mars. Their mass will remain the same, and that's important to know for things like acceleration.
Additionally, figuring out the mass of something in space is different than on a planet since there's no gravity pulling down on the object. To figure out the mass of something in space, you use what's called an inertial balance, a device that vibrates or swings as something is measured. This process of determining's something mass involves tracking the rate of oscillation when an object is placed in the balance. When you add more mass to the balance, it will oscillate more slowly; if you remove mass, it will oscillate more quickly. Knowing the amount of time it takes to complete a determined period of oscillations will help you determine the object's mass.
The video below shows how this process works on the International Space Station using an actual astronaut.