continuous spectrum:

In physics, continuous spectrum refers to a range of values which may be graphed to fill a range with closely-spaced or overlapping intervals. The term is derived from the use of the word spectrum to describe the 'ghost-like' rainbow which appears when white light is shone through a clear scattering medium, such as water droplets or a prism.

Colors are red,orange, yellow, green, blue, indigo, and violet. They can show up together and overlapping, or individually.

The idea of a continuous spectrum can be viewed as "a continuous set of eigenvalues" — an apparent contradiction in terms. Eigenvectors occur discretely. The mathematics of continuous spectra belongs to spectral theory, a branch of functional analysis.

http://en.wikipedia.org/wiki/Continuous_spectrum

emission spectrum:

An element's emission spectrum is the relative intensity of electromagnetic radiation of each frequency it emits when it is heated (or more generally when it is excited).

When the electrons in the element are excited, they jump to higher energy levels. As the electrons fall back down, and leave the excited state, energy is re-emitted, the wavelength of which refers to the discrete lines of the emission spectrum. Note however that the emission extends over a range of frequencies, an effect called spectral line broadening.

The emission spectrum can be used to determine the composition of a material, since it is different for each element of the periodic table. One example is identifying the composition of stars by analysing the received light.

An absorption spectrum occurs when light passes through a cold, dilute gas and atoms in the gas absorb at characteristic frequencies; since the re-emitted light is unlikely to be emitted in the same direction as the absorbed photon, this gives rise to dark lines (absence of light) in the spectrum. The light emitted from an excited atom can not be directed toward the observer, so the light appears to be missing from the continuous spectrum.

http://en.wikipedia.org/wiki/Emission_spectrum

Are you doing higher physics in Scotland by any chance?! Thats exactly the same thing i was asked in the homework this week too! Write back! =]

emission spectrum: The pattern of spectral emission lines produced by an element. Each element has its own unique emission spectrum
Continous spectrum: A spectrum that contains an entire range of colours and not just separate wavelengths.

A continuous spectrum is all wavelengths of radiation, an emission spectrum is the result of matter being heated and emitting electromagnetic radiation at discreate wavelengths according to the allowable energy levels of it's electrons