Alternate Names
PVC, Vinyl, Polymer, Poly, Plastic, Non-Abrasive, and Technical. These are all different descriptors for roughly the same thing.
By the way, my daughter has about 3,000 little novelty erasers shaped like hamburgers and strange Japanese hamsters. While these may be vinyl and some are even white, they are not what I'm talking about here.
Brands
Staedtler, Pentel , Tombow, Campus, Lyra, Faber-Castell, Nayana ... these are just the top names, there are tons more. They're all slightly different and some work better than others, but I've never encountered a white polymer eraser that didn't do a good, scratch that, great job of erasing basic work marks.
Defining Features
This is a soft plastic, almost rubbery eraser which contains no abrasive pumice or grit. It feels smooth and buttery when rubbed against paper and it leaves a minimal amount of debris.
Best Used On
Excellent for graphite (pencil lead) in any hardness. Moderately effective on waxy colored pencil and firm chalk pencils. Excellent for finger and hand smudges that collect on the borders of your work.
If I need to erase something, this is the first eraser I try because it's gentle. I may end up moving to something more abrasive for stubborn marks, but I always begin the process with my white PVC eraser.
Styles
For years PVC erasers came in brick style only, usually with a cardboard sleeve which kept large bricks from cracking. For greater control, try a stick version. White vinyl erasers are pretty standard on top quality technical pencils but I've also seen them on the disposable PaperMate level mechanical pencils. Artist-grade electric erasers use PVC erasers. The most recent development has been a micro sized PVC eraser in pen form, the Tombow Mono Zero eraser, which is excellent when working in small areas.
Note: there are also very similar PVC-Free white erasers on the market. For the record, that's the only white eraser that I've ever hated. It was oddly soft and it developed small cracks on the first use. I quit using it when large chunks started coming off, about 2-3 weeks into daily use.
Price Range
Very inexpensive. Small bricks and sticks are often found in value multipacks for under $1 per eraser. The Tombow Mono Zero eraser is around $5.
Availability
Very widely available. Art stores, craft stores, office supply stores, and in the office supply area of many big-box retail chain stores. Online at numerous retailers.