Many of the works in “Mischief” resemble aerial landscapes of the American Southwest. (Lee Haner)

There are two strong reasons for fans of painting to visit the American University Museum: Lee Haner and Timothy App.

At first glance, their shows could hardly seem more different. Haner’s “Mischief,” which features only recent work, consists of roughly textured, earth-toned abstractions that evoke the rocky landscape of the Southwest. App’s retrospective assembles work from a 45-year career and seems the product of a power-mad minimalist interior decorator, or a Mercedes-Benz engineer. Anchored by sober shades of gray, its muted palette articulates a rigidly proscribed, almost machinelike geometry. Called The Aesthetics of Precision,” the show betrays barely a single visible brush stroke.

There are, of course, some similarities. Both painters have deep local roots as teachers: Haner taught for several years at American University, App at the Maryland Institute College of Art in Baltimore. And both men love paint, though each has chosen a very different way to show it.

For App, paint’s appeal derives from what he calls its “emotive” quality. But his is no splashy Pollockian expressionism. He applies his medium like a house painter, using masking tape to create clean, straight, dripless edges and covering his tracks as he goes. The earliest work in the show, “Untitled (Grey)” from 1968, is a monochromatic study in almost surface-less subtlety. The only visual interest that breaks the monotony of the painting is its two canvases: A smaller one is nestled snugly inside a square hole that has been carved out of a larger one.

So where, exactly, is all the emotion? It’s in the color.

App does paint shapes — mostly rectangles, triangles and semicircles — yet it is his soft-spoken use of grays and grayed-down reds, whites, aubergines and other hues that gives his work its surprising power. Be patient; the show takes a while to detonate. This is art that builds slowly to a climax, like a depth charge, but only if you give it time.

Aside from a few shaped canvases and two pieces from the 1970s in which you can actually see brush strokes (“Ways of Water” and “Lunarsea”), there’s a uniformity to “The Aesthetics of Precision” that can seem numbing at first. But it would be a mistake to dismiss App as having made the same painting over and over again, and not just because there are infrequent flashes of variety. A few paintings, inspired by time he spent in Santa Fe, N.M., could almost be called colorful.

Rather, the deliberate restraint of his pictures both reins in and reveals a hidden turbulence that lies well below the surface and that complicates and enriches their tranquillity.

The accusation of sameness could be leveled against “Mischief,” too. Most of Haner’s paintings resemble aerial photography or topographical maps, varied only by subtle differences in terrain. But unlike App, Haner is a protean stylist. Over a long career, his art has taken many forms.

Haner’s latest body of work takes its name not from a sense of play — though his work can be funny — but from a sense of harm. The original meaning of the word “mischief” refers to damage or injury. And, indeed, the works in this show are characterized by gouges that have been scratched into their surfaces, which have been thickly built up with layers of gesso and paint.

Because the paintings look like aerial landscapes, the marks evoke roads or, in some cases, cave paintings and even geoglyphs (large land “drawings” that can be seen only from the air). Coincidentally, Haner is also inspired by the landscape of Santa Fe. Yet if Haner is using paint to evoke emotion, our response is mixed. His pictures are gorgeous, yes, but you can’t help looking at them without feeling a twinge of sadness. After spending a bit of time with this show, the marks begin to resemble scars on Mother Earth.

The experience is one of pleasure mixed with pain.

Neither of these two painters’ work is purely abstract. App’s art celebrates a kind of pristine architecture, while Haner’s offers a window onto a wilder natural world.

In each case, the hand of man is evident. For App, it’s evident in the way his paintings try to contain — or perhaps even tame — deep feeling. For Haner, it’s in the way his paintings evoke the marks that will linger on the surface of our home planet long after we have left it.