What is the difference between RVR and visibility?
The definitions are somewhat different:

Visibility for aeronautical purposes is the greater of:

the greatest safe distance at which a black object of suitable dimensions, situated near the ground, can be seen and recognised when observed against a bright background;

the greatest distance at which lights in the vicinity of 1000 candelas can be seen and identified against an unlit black background.


Runway Visual Range (RVR) is the range over which the pilot of an aircraft on the centre line of a runway can see the runway surface markings or the light delineating the runway or identifying its centre line. (ICAO Annex 3)

(Visibility on SKYbrary)
The RVR is specific to the runway and its actual lighting system (i.e. can be different for different runways of the same airport at the same time), where visibility only refers to the general range an object or light can be seen in the current conditions.

RVR can be measured along the runway, e.g. using a transmissometer:

RVR equipment is typically found at larger airports, and RVR visibilities can be reported for up to four designated runways at an airport. It's calculated using sensors like this:



The sensors are located along the runway, and they're approximately 14 feet higher than the centerline of the runway.
On most runways equipped with RVR, there are three sensors: a touchdown sensor, a mid-point sensor, and a rollout sensor.

(boldmethod.com)
On the other hand, visibility is typically measured by detecting scattered light from a strobe (scatterometer):

The most common method of measuring the extinction coefficient is the forward scatter system. A high intensity xenon strobe transmitter directs a beam of light in the visible spectrum at the air close to the sensor and a photo diode at the adjacent receiver is used to detect the amount of light received. The extent of scattering is increased by the presence of particles of water, dust, sand or smoke. The use of transmitted light within the visible spectrum allows this type of instrument to most accurately simulate human perception of visibility. The range of visibility for which a measurement can be derived is typically between 15/20 m and 20/30 km with an accuracy up to 10 km of +/- 10%. A typical instrument is illustrated below:


(Automated Cloud Base and Visibility Measurement on SKYbrary)
For more details on measurements, see:

How is the visibility at airports measured?


How do visibility and RVR compare?
The ICAO Aerodrome Meteorological Observation and Forecast Study Group published A Comparison of RVR and Visibility Reports:

Previous studies have shown that the reported value of RVR is typically higher than the associated visibility value. [...] These findings are consistent with the fact that the assessment of RVR takes advantage of high intensity runway lights while the visibility assessment is based upon lights of moderate intensity.
[...]
A comparative review of the 5,662 METAR / SPECI from three aerodromes over a five year period that contained both prevailing visibility and RVR information revealed that, in equivalent terms for 2825, or 50 per cent, the RVR report was less than the visibility.
[...]
meaningful predictions of RVR from prevailing visibility reports can only be  accomplished if the assessment of both RVR and visibility is by reference to common sensor(s).

It seems, RVR is typically higher than visibility, but only if the runway lighting system is using high intensity lights.