This may be a simplistic answer, but I'll try to add some substance to the essential response, which is that the term "Gilded Age" does not imply a "golden age" of fabulous wealth and riches for all. The term comes from the book The Gilded Age: A Tale of Today by Mark Twain and Charles Dudley Warner, published in 1873, and in this context refers to a period which appears golden on the outside, but is really hiding a rotten interior: hence gilded, not golden. In fact, the period between 1870 and 1900 (most historians seem to pin the Gilded Age between 1877, the end of Reconstruction, and 1900, but I'll give 1870 as the rough start here) was rife with massive income inequality, economic depressions, and labor struggles. The Panic of 1893 was preceded by the Panic of 1873, and for the average person the period would've seemed more unstable and violent (strikes such as the 1877 Railroad Strike and the 1894 Pullman Strike were just two of the largest strikes of the period), with weak presidents, political parties seemingly torn by graft particularly in cities such as New York, the coming of Jim Crow and the final legalization of racial segregation in 1896, and constant economic pressures and labor issues. While there were some who benefited from this environment, they were mainly the upper-upper-upper class, robber barons like Jay Gould and industrialists who were really hardly any better like Andrew Carnegie and John D. Rockefeller. Hence "gilded": if you just look at the fabulous mansions in Newport and read about the exploits of socialites like Alva Vanderbilt, it seems like a period of insane wealth, security, privilege, and pleasure. And while this was a time of increasing leisure time for many Americans and lowered work hours and higher wages in some industries (largely thanks to the intense labor agitation and unionization of the era), the experiences of the 1% tend to cloud out much of the reality.

As for the "Gay Nineties", that's largely a nostalgia term that was coined decades after the fact to describe the period. During the 1920s, the 1890s began to be seen as a safe, peaceful period without war or strife (remember this was the childhood of many members of the Lost Generation, who were shaped by their experiences in World War I, the Spanish Flu pandemic, the immediate economic depression post-war, and other upheavals). To many in the 1920s and through the 1950s, the 1890s seemed blissfully innocent and charming compared to the terrors of modernity that seemed to come afterwards. Plus, a lot of people just appreciated the aesthetic, as depicted in movies like The Strawberry Blonde (1941), Meet Me in St. Louis (1944), or Lady and the Tramp (1955) (Walt Disney, born in 1901, was a particular fan and promoter of the Gay Nineties aesthetic, which is why Main Street at Disneyland is designed in the style.) In this sense, it's not too dissimilar to the 1980s nostalgia which has been so prevalent since the mid-2000s, which tends to view the decade as a period of joy, color, pleasure, and amazing pop culture while ignoring that it was a tense time globally and domestically for the majority.