Relativistic mass

Relativistic mass is a mass of a particle any observer is seeing in her/his reference system of coordinates. It is the same as invariant mass of the particle multiplied by $\gamma$ factor that tells how much mass a moving particle has in relation to invariant mass (called sometimes the rest mass).

It means that for different observers the relativistic mass may be different which would mess the physics a little bit, and that's why physicists decided to introduce the notion of invariant mass that for every observer is the same and simplify calculations in physics. Presently when physicist says "mass" she/he always understands it as invariant mass though it is not that simple when non physicists get into a discussion since many of them assume that "mass is growing with its velocity" as it was understood still in Einstein's times. Of course the physics is the same but the terminology changed. Now the "mass is growing with with its velocity" is called by physicists "energy" and relativistic mass or "inertial mass" by everybody else.

The "mass" on the right side of Einstein's equation $E=mc^{2}$ is invariant (or rest mass) for a physicist and generally relativistic mass, or "inertial mass", for non physicists, which is rather non intuitive arrangement but luckilly the Einstein's equation works for both (unless one wants spacially accurate terminology, which then may to involve also curvatures of spacetime).