Topiary shapes a plant in three dimensions. Espalier trains that same plant flat against a plane, and those two sentences are most of topiary vs espalier right there. Pollarding is a third thing again. It isn't a shape you carve at all, it's a cut you repeat, taking the past season's growth back to one fixed point every year.
None of these forms could have happened on its own. A shrub doesn't grow into a cone, and an apple tree doesn't lay its limbs out in a single flat plane against a wall. Someone put it there and someone keeps it there. Each word names the form a gardener is holding the plant in, plus the cutting that holds it, which is why the labels are worth getting straight before you pick up the shears.
Topiary is the practice of pruning shrubs or trees to create unique shapes or living sculptures, in the wording NC State Extension uses. The work is done with shearing or heading-back cuts. You cut the outside of the plant back to a line you have chosen, then you do it again, and the plant slowly fills that line. Hold a shape like that and you have signed up for frequent pruning for as long as you want the shape.
Espalier is formal two-dimensional training of a plant against a flat plane. A wall, a fence, a set of wires strung between posts. Everything the plant does happens in that one plane, and anything that heads out toward you gets cut off. Set topiary vs espalier side by side and the split is depth. One form keeps it, the other gives it up. A formal espalier also asks for the same frequent pruning a topiary does, because flat only stays flat if you keep cutting.
Pleaching is the one people mix up with espalier, and the pleaching definition is narrower than most gardeners expect. It's weaving branches together to form a living wall or fence. Branches from neighboring plants meet, cross and grow into each other, so a row of trees reads as one green screen rather than as separate trunks with gaps between them.
The pollarding meaning is the tightest of the four, and it says nothing about shape. You head all annual growth back to the same point each year. Same point, same season, every single year. Skip a few of those years and you are no longer pollarding, because the form is only a form while the yearly cut keeps happening.
Topping doesn't belong on that list at all. It sits apart from every trained form above as an inappropriate pruning practice, not a fourth style with a fancier name. So if a crew offers to top your shade tree and calls it pollarding, those are two different things, and only one of them is a technique.
Pick by the form you actually want to end up with. A shaped focal point or a living sculpture means topiary. Something formal and flat held against a wall or a wire frame means espalier. A row that closes into one green screen means pleaching. And if what you want is the whole year's growth headed to one fixed spot, over and over, that's pollarding, and the calendar matters more than the outline.
The honest part of the topiary vs espalier question is the upkeep. Both need frequent pruning to keep their shape, so neither one is a plant-it-and-leave-it choice. Pick the form you'll still be willing to cut in five years, not the one that looks best in a photo.
Read the full article: Topiary: How to Shape Plants Without Killing Them