There's no splitting hairs. Pumps move fluid, true enough. But the output side of the pump is under pressure, and fluid is being moved to a location. Pumps usually don't draw from a source, they push to a source.
This is important. It's for this reason that many low pressure pumps and engine driven pumps don't have the ability to suction feed, or can do so for only a short period of time. These pumps are life limited on suction feed. On a suction feed operation, the pump is "pulling." However many of these systems, indeed most all turbine installations, need to have fuel fed to them under pressure. The purpose of the pump is to push fuel somewhere, under pressure, at a higher pressure than it's taken in. Boost pumps are there to boost fuel pressure and maintain a line pressure. Often these pumps are submerged, and are being fed by a resorvoir or tank which surrounds the pump. On more complex aircraft that utilize jet pumps, this is handled a little differently, but many aircraft still use submersible pumps.
These pumps draw off surrounding fluid, or a feed to the fluid, which often arrives under it's own head pressure from tank pressure or the weight of the fluid. From here it pumps, or pushes the fluid under pressure to a destination. That may be another customer pump, or an accessory/engine pump, such as an engine driven low pressure pump.
In many cases, the purpose of this pump isn't just to push fuel to the engine, resorvoir, header tank, or other pump, it's there to push with pressure, or to pressurize the fuel lines to prevent vapor lock and pump cavitation.
The output pressure of the fuel pump, by the nature and general definition of a pump, is higher than the inlet, which may have little or no pressure at all. The pump is there to push fuel to a new destination. Some pumps pull, most push.
The reason for the pump is the determining factor, as well as it's location in the system.
Suction pumps, on the other hand, serve the primary purpose of pulling fluid from one location and then providing motive force to get it some place else. Their primary purpose is generally to draw fluid from a source, as opposed to supplying it under pressure to another source. In a typical oil system, the engine driven oil pump serves as a pressure pump to force oil under pressure to the various bearings, ports, and galleys in the engine. Scavenge pumps retrieve this oil, sucking or pulling it from collection points, and returning it to supply the pressure pump via resorvoirs, oil coolers, and other interim stages or devices.
Hydraulic pumps push fluid under pressure to accumulators, actuators, and hydraulic lines, accessories, etc. The purpose of the pump is not to pull fluid through the system, and system customer functions are not actuated by fluid being pulled through the system. These are actuated by fluid being pushed through the system under pressure, typically either 1,500 lbs or 3,000 lbs.
Weather the system pulls or pushes fluid, and pumps do both, is important to it's proper operation, and the understanding thereof.