The electromagnetic spectrum is the range of all possible electromagnetic frequencies. The "electromagnetic spectrum" of an object is the characteristic distribution of electromagnetic radiation from that particular object.
The electromagnetic spectrum extends from below frequencies used for modern radio at the long-wavelength end through gamma radiation at the short-wavelength end, covering wavelengths from thousands of kilometers down to a fraction the size of an atom. It is thought that the short wavelength limit is in the vicinity of the Planck length, and the long wavelength limit is the size of the universe itself see physical cosmology, although in principle the spectrum is infinite and continuous.
Electromagnetic radiation can be described in terms of a stream of photons, which are mass less particles each traveling in a wave-like pattern and moving at the speed of light. Each photon contains a certain amount or bundle of energy, and all electromagnetic radiation consists of these photons. The only difference between the various types of electromagnetic radiation is the amount of energy found in the photons. Radio waves have photons with low energies, microwaves have a little more energy than radio waves, infrared has still more, then visible, ultraviolet, X-rays, and the most energetic of all gamma-rays.
Actually, the electromagnetic spectrum can be expressed in terms of energy, wavelength, or frequency. Each way of thinking about the EM spectrum is related to the others in a precise mathematical way. So why do we have three ways of describing things, each with a different set of physical units? After all, frequency is measured in cycles per second which is called a Hertz, wavelength is measured in meters, and energy is measured in electron volts.