It is important to know which type of measurement to use in your research/experiment and not to confuse those types. Normally we would talk of Numerical (Score) and Nominal (Category) types of measurement; numerical then can be of three types itself: ordinal (rank), interval and ratio measurement types.
Assigns a category to which a particular case belongs; this is also called qualitative measure. Categories could be, for example, participants' occupations (is a person an actor? or a builder?) . There are no numbers involved as such, unlike in the numerical measurements.
2. Numerical measurement
Assigns numerical value; also referred to as quantitative measure. For example, IQ is measured numerically, as its value is determined by a number (in a psycho jargon, score). Thus, these numbers quantify the variables. Typically, physical measures such as weight, temperature, length etc. are quantified numerically.
Numerical measurement in itself also has three types (you didn't think it was that simple did you?)
2.1. Ordinal measurement
Also known as rank measurement. The actual values of scores are either unknown or don't matter, and the only information this type of measurement provides is which score is the smallest, the next smallest, the next smallest - and up until the largest one. It creates a set of ranks from smallest to the largest, and their numerical value is 1, 2, 3 etc.
2.2. Interval measurement
The easiest way to understand this type of measurement is to imagine any physical measurement scale such as thermometer or a tape measure: the intervals between numbers on this scale are all equal.
2.3. Ratio measurement
This is basically the same as the Interval measurement, but with the absolute zero point known - thus, it is possible to work out the ratios. Temperature, for example, is NOT a ratio measurement since it does not have an absolute zero: 0 degrees Celcius is just a point on a continuous scale of temperatures. Distance, however, has an absolute zero, hence it is possible to say that, for instance, 20m is twice as long as 10m.