A Chinese-style cameo vase, c. 1890.

Goblets, vases, bottles, bowls—in "East Meets West: Cross-Cultural Influences in Glassmaking in the 18th and 19th Centuries," some 70 vessels that once held drink, food and flowers now pour forth a tale involving European alchemists, Asian artisans, a Dutch Jesuit, French designers and a Chinese emperor with a penchant for the new and exotic.

Given that the show is about art, technology and design crisscrossing the globe, it might seem appropriate that the display space straddles one of the thoroughfares in the Corning Museum of Glass. But this is unfortunate, for it is all too easy to walk past without realizing that 18th-century Chinese vases on our right bear a relationship to a white Dresden flask across the passageway.

The key, we discover, lies in the material itself. When Chinese porcelains made their way to Europe via the Silk Road, Europeans quickly began trying to make their own. But they assumed porcelain was vitreous, not clay-based. After 15th-century Italian alchemists developed an opaque, white glass they called "lattimo" (from latte, meaning milk), others refined the process. In 1680, German polymath Johann Joachim Becher boldly declared milk glass superior to porcelain.

Here we see why: Three cases contain delicate white vessels decorated with floral and Asian-inspired motifs that even curator Florian Knothe cannot distinguish from porcelain without checking the underside for the scar left by the blow-pipe.

Because they are grouped by place of origin, we also see differences among European markets in the last half of the 18th century. The English vases emulate Chinese imports in both shape and decoration, while beautifully gilded and decorated scent bottles echo the squared-off lines of imported snuff bottles. The Italian and Central European pieces, by contrast, are mostly standard European ware—cups and saucers, tankards, covered bowls, even cutlery—sometimes decorated with pagodas, robed figures and Chinese landscapes.

Their purpose was the same: to offer affordable substitutes for porcelains. The difference was that English glassmakers were competing with East India Company imports, while on the Continent, glassmakers had more immediate competition: Since 1710, two chemists had been making clay-based porcelains in Meissen, Germany.

By the 1880s, however, Western powers had forced China and Japan into trade agreements. As exotic Asian treasures swept the Continent, French designers joined their English peers with imitations not just of porcelains, but of carved elephant tusks, rock crystal and jade—even, as this section shows, the occasional riff on Chinese glass. But first, we need to cross the thoroughfare to the Asian side.

Here, the Chinese pieces date from the reign of the Qianlong Emperor (1736-1795), a ruler known for his curiosity about Western technologies, while the handful of Japanese works date from the decades following the 1854 trade treaty with the West. What is most striking is that the Japanese wares emulate European cut crystal, while the Chinese pieces adapt European technology to manufacture Chinese designs.

Once again, cherchez the market. Cut crystal was all the rage in 19th-century Japan, so glassmakers made more affordable substitutes, like the Satsuma set of stacking cups and matching decanters. In 18th-century China, on the other hand, opaque milk and colored glass was a luxury—whose secrets Dutch Jesuit missionary Kilian Stumpf first brought to the imperial court in the 1680s. Among other things, we see variegated works that illustrate how Chinese glassmakers transposed techniques from lacquerware: A long-necked bottle in opaque yellow glass, for example, was once covered with layers of blue and green glass that a master craftsman then cut away to leave a floral relief.

An 1890 red-and-white vase in the English case across the way turns out to be a riff on this technique: The English master craftsman sandwiched a layer of clear glass between the white body and the red overlay. After cutting away the floral motif, he etched the clear glass for added depth and texture. Intriguingly, an 18th-century Chinese table screen shows similar inventiveness: Its maker took a watercolor painting of a domestic scene, cut along its contours, then placed it like a découpage between two panels composed of thin glass rods. Because the rods run diagonally in opposite directions, they texture the negative space with a faint, crisscross pattern.

If the show is weighted more toward Europe than Asia, it is partly due to the strengths of the museum's collection, partly to the need for more research. "The composition of these vases," says Mr. Knothe, pointing excitedly to two 18th-century enameled glass vases made in Beijing, "is almost identical to the chemical composition of the 1710 Dresden piece." That would be the white Dresden flask. "Yet," Mr. Knothe adds, it is "different from English white glass." Does that mean that Stumpf brought the Dresden recipe for milk glass to China? "We cannot say yet for sure." But you can tell he'd really like to.