Do decibel (dB) and decibels relative to full scale (dBFS) refer to the amplitude or intensity of sound? This is quite confusing as several websites present conflicting information.
eg. https://en.wikipedia.org/wiki/Decibel
"dB(full scale) – the amplitude of a signal compared with the maximum which a device can handle before clipping occurs."
http://www.physicsclassroom.com/class/sound/Lesson-2/Intensity-and-the-Decibel-Scale
"This type of scale is sometimes referred to as a logarithmic scale. The scale for measuring intensity is the decibel scale"
 A: It can refer to either.  This quote from the first Wikipedia article you linked sums it up pretty well: 

There are two different scales used when expressing a ratio in decibels depending on the nature of the quantities: field, power, and root-power. When expressing power quantities, the number of decibels is ten times the logarithm to base 10 of the ratio of two power quantities.[2] That is, a change in power by a factor of 10 corresponds to a 10 dB change in level. When expressing field quantities, a change in amplitude by a factor of 10 corresponds to a 20 dB change in level. The extra factor of two is due to the logarithm of the quadratic relationship between power and amplitude. The decibel scales differ so that direct comparisons can be made between related power and field quantities when they are expressed in decibels.

So when talking about power or intensity level, you use a coefficient of 10 in front of your logarithm.  For things like amplitude, sound pressure, voltage, etc., you use a coefficient of 20 due to their quadratic relationship to the previously mentioned quantities.
  As an example, say you have a sound source that has intensity $I$ some distance $r$ away from the source.  The corresponding pressure at that distance, $p$, is $\propto \sqrt{I}$, or in other words, 
  $$I = kp^2$$
For some proportionality constant $k$. 
If we want to find the intensity level $IL$ of our source at $r$ with respect to some reference intensity $I_0$, we would calculate 
  $$IL=10\log_{10}\left(\frac{I}{I_0}\right) \tag{1}$$
We could then define a corresponding reference pressure $p_0$ such that $$I_0=kp_{0}^{2},$$
and find a sound pressure level $SPL$ with respect to this reference pressure by substituting in $I=kp^2$ and $I_0=kp_{0}^{2}$ into $(1)$:
$$ SPL=10\log_{10}\left(\frac{kp^2}{kp_{0}^{2}}\right)=10\log_{10}\left(\left(\frac{p}{p_{0}}\right)^2\right)=20\log_{10}\left(\frac{p}{p_{0}}\right)$$
Where the last equality comes from the power rule for logarithms of any base $b$:
$$\log_b\left(a^n\right)=n\log_b\left(a\right)$$
