When I read the description of VSOP87, I find out that there is a file with "variables of date" and a file with "variables J2000". In Astronomical Algorithms of J. Meeus I can find out how to use the variant "Variables J2000". But I don't know, for what is "variables of date" good.
The description just says "apply for each term the formulae (1) or (2) with T=(JD-2451545)/365250". So I have always to calculate the JD for both variants.
The difference between the equinox of J2000 and the equinox of date is precession. You can read about precession, and how to calculate precession of coordinates between epochs, in chapter 20 of the Meeus book you mentioned.
You always need the actual Julian Day number (JD) to calculate a planets position, but the epoch defines which reference directions are used for the coordinates.
If you want to plot an object, such as a planet, on a star chart you would use the chart's epoch, usually J2000. If you want to point your telescope at an object in the sky you would use coordinates for the epoch of date. I have not used any of the VSOP models recently, but I recall they provide ecliptic coordinates in either spherical or rectangular format. They also provide these coordinates in both epoch J2000 and those already precessed to the epoch of observation date.
Precession of the equinox is a bit under 50 arc seconds, or about 0.8 arc minutes per year. So it does not take too many years for positions in the sky to be slightly shifted from the J2000 epoch.
