The metes and bounds of those two descriptions are nebulous at best.
In my experience, people who work on the production of movies - anyone who works in the production, from the lowliest PA (production assistant) through the grips, editors, actors, cameramen and such - all work in "film production".
A producer - will be a person who has more oversight over the production. Depending on how sophisticated the production is, a producer might be an independent producer who does everything from writing, casting, camera, editing and trying to sell the production. For a large production, only the very high-up money men or managers are called producers.
A video producer - might be someone who works coordinating video segments for a local news show, or who works for a wedding video production company coordinating, shooting, editing and such, or who oversees the production of commercial advertising bits.
Someone who lists, "video production" experience - might mean that they were an assistant editor or a lowly PA or 'script girl' or continuity assistant - or they might be the production manager or cinematographer or executive producer of something bigger.
Really, the important stuff is in the details - more than the titles. Hopefully these people will have listed some specific details describing their experience.