Generally, Signal Strength is simply a measure of the power of a signal. If the measurement is expressed in watts or some variant thereof, the measurement implies the the amount of heat that would be dissipated if all of the energy was terminated in a purely resistive load. Signal Strength does not measure the integrity of information that may or may not have been encoded or modulated into a radio wave. In the case of OTA DTV, power in units of dBm is common. Not as common, but still used are units of milli-volts and dBmV, and because the system impedance is nearly universally 75Ω, a direct conversion to units of power can be made using Ohm's and Watt's laws.
http://en.wikipedia.org/wiki/Decibel
Signal Quality generally refers to some sort of measurement that describes how well the measured signal resembles the original signal transmitted, or, how likely the original information may be decoded or demodulated without error. A signal can be altered, distorted or interfered with in many ways, therefor, the quality of a signal can be measured in many ways. Signal to noise ratio is a measure of how much noise and/or interfering signal has been added to the desired signal. In the case of digital signals, error rate is often used as a measure of quality.
An analogy exists in the audio world. As you are sitting at a stop light, listening to the stereo system in the car behind you, you are likely quite aware of how loud the sound is. Just because it's loud enough for you to hear, does not mean you can understand lyrics or even identify the song being played (perhaps the rattling fender sound is a source of interference). You could measure the power of the audio signal with a sound level meter, which may be helpful to understand whether you are at risk of damage to your hearing, but that simple 'sound strength' measurement will not quantify the quality of the audio. Measuring the ratio of desired signal verses noise plus interfering signals is a more complex measurement that would be an example of how to quantify quality.
This link
http://www.guitarkitbuilder.com/cont...d-oscilloscope offers a visual of audio distortion. In the case of the guitar, distortion is desirable at times, if it can be controlled and used artistically. When trying to send information error free, distortion would not be desired or helpful.