Fuel vs. Propellant I am looking at http://nathangeffen.webfactional.com/spacetravel/spacetravel.php.
My understanding that his fuel requirements are based on the energy needed to move the spacecraft + fuel the distance entered at a constant acceleration entered (and takes into account the diminishing mass of the spaceship as fuel is expended).  So far so good.
What I am unclear about is that the only thing mentioned is fuel... but not propellant.  Does this site assume that the fuel IS the propellant (or that propellant mass is included in the fuel?)
 A: With regard to spacecraft, "propellant" is an all-encompassing term that describes all of the stuff that describes all of the stuff the spacecraft carries that will eventually be ejected to generate thrust.
In bi-propellant chemical engines used to launch spacecraft into space, the propellant comprises the fuel (the stuff that burns in the presence of an oxidizer) and the oxidizer. In monopropellant chemical engines such as hydrazine passing through a catalyst bed, the hydrazine is the propellant. In cold gas systems, the compressed gas is the propellant. In ion propulsion systems, the xenon (or whatever) that will eventually be ejected is the propellant. In a hypothetical matter/antimatter propulsion system, the matter and antimatter that will eventually be ejected as photons are the propellant.
Some people such as the referenced website use "fuel" as the all-encompassing term. Strictly speaking, that's incorrect. "Fuel" refers to the reducing agents used in a chemical rocket that are oxidized by an oxidizing agent. The fuel (reducer) and the oxidizer collectively form the propellant in a bi-prop chemical rocket.
That said, it's best to not be so pedantic, particularly when discussing the ideal rocket equation or its relativistic equivalent. "Fuel" in this context is a synonym for propellant.
A: The site makes a rather odd presumption, which is contained in the line "Fuel conversion efficiency". This assumes that fuel mass is converted to ship kinetic energy at a fixed rate, or $$ \Delta KE = \eta \Delta mc^2$$ where $\eta$ is the conversion efficiency. This is not the way things are usually expressed. Ordinarily, rocket fuel/engine systems are characterized by specific impulse, change in momentum per unit fuel mass consumed, and as velocity increases the effective thrust decreases. However, the page contains the hidden assumption that the "rocket" involved actually uses a photon drive, and this accounts for the discrepancy (since the speed of light is constant for all observers).
Otherwise, David Hammen's answer is excellent.
I would add, though, that non-chemical drives make a very clear distinction between fuel and propellant. In these systems, the fuel is typically radioactive materials, while the propellant is the reaction mass tossed out the back, which may well be some material such as caesium, indium or xenon. See the Wiki page on ion thrusters for a starting point.
