The sound levels to which most mammals are sensitive extend over many orders of magnitude and, for this reason, it is convenient to use a logarithmic scale when measuring sound. Both Sound Pressure Level (SPL) and Sound Intensity Level (SIL) are measured in decibels (dB) and are usually expressed as ratios of a measured and a reference level:

Sound Pressure Level (dB) = 20 log (p/p_ref) where p_ref is the reference pressure

Sound Intensity Level (dB) = 10 log (I/I_ref) where I_ref is the reference intensity

In other words, the decibel is 10 times the log of the ratio of two intensities, and 20 times the log of the ratio of two pressures. The units for both SPL and SIL are dB relative to the reference intensity (often abbreviated as dB re 1µPa or dB//1µPa). Whenever "level" is added to the terms sound intensity or sound pressure, it usually implies that the measurement is in decibels. Because decibel implies a ratio of two values (and therefore a dimensionless measurement), SPL and SIL are equivalent when measured in decibels.

Because the dB scale is relative, reference levels must be included with dB values if they are to be meaningful. The reference levels for SPL and SIL are equivalent but are reported in different units.  The commonly used reference pressure level in underwater acoustics is 1 µPa while the reference level in air is 20 µPa (which is roughly the human hearing threshold at 1000 Hz). The reference intensity in water is

I_ref = p² _ref / (r_water c_water) = 6.7 x 10^-19 W/m²

where reference pressure in water (p_ref) is 1µPa rms,

and the density of water (r_water) is about 1000 kg/m³,

and the speed of sound in water (c_water) is about 1500 m/s.

Historically, the reference intensity in air was the sound intensity barely audible to humans,
1 E ^-12watts/m² or 1 pW/m². (A painful airborne sound to humans is about 10 watts/m²).

When quoting source levels, the distance from the source for that reference level must also be cited in addition to the reference level. Typically the units of SIL are dB relative to the reference intensity at 1 meter (e.g., 20 dB re 1µPa @ 1m) - i.e. how intense the sound would be were it measured 1 m from the source. In practice, one can rarely measure source level at the standard 1 m reference, so that source levels are usually estimated by measuring SPL at some known range from the source (assumed to be a single point), and the attenuation effects predicted and subtracted from the measured value to estimate the level at the reference range of 1 m.

Ideally, it is Sound Intensity Levels that we’d like to measure. However, it’s easier to measure sound pressure than sound intensity, so we measure pressure, and from that infer intensity. Within the same medium, sound intensity or power is proportional to the average of the squared pressure:

I µ p²

therefore

SIL(dB) = 10 log (I/I_r) = 10 log (p² / p² ) = 20 log (p/1µPa) in water

or = 20 log (p/20uPa) in air

In other words, once we start using the decibel scale, SIL and SPL are pretty much the same thing.