I looks as if you are reading some literature on protein separations. "Conventional chromatography" probably refers to the particle size. Larger particles, say 30 micron or larger, are used without sophisticated equipment, such as high-pressure pumps and automated injectors etc. If the particle size is large enough, you can simply use glass columns and let the solvent drip though the column driven by gravity.
High-performance liquid chromatography uses small particles, between 1.5 micron and 10 micron, today most commonly 5 micron particles. This requires pumps with the capability of high pressure, commonly up to 400 bar. With this requirement goes along a sophisticated instrument that can run automatically, i.e. inject samples and collect data in unattended mode.
Fast Protein Liquid Chromatography or FPLC is in principle the trade name given to a branch of HPLC by an instrument manufacturer who has dedicated his instruments to protein analysis. It is in principle a HPLC instrument, but built from mostly non-metallic parts. There are also some operational differences between protein HPLC and small molecule HPLC, but this has really nothing to do with FPLC.