Gravity waves are ripples in the atmosphere, whereas gravitational waves are ripples in the space-time fabric.
Gravitational Wave Description 1
Gravitational Wave Description 2
Gravitational Wave History
Collaborations Between Observatories
Canceled Space Interferometer
Burst wave Description
The New Era
So, gravitational waves.
Back in 1893, Oliver Heaviside discussed gravitational forces. By November of 1916, Einstein published the General Theory of Relativity. Soon after, he speculated that gravitational waves existed, like Henri Poincare had done in July of 1905. Other scientists, and Einstein, actually doubted the existence of these waves. In 1936, after becoming aware of a misinterpretation of his formula, Einstein became convinced gravitational waves exist. Then in 1956, Felix Pirani published a paper that got rid of a coordinate system problem and showed that particles oscillated (following a geodesic) as it passed by. But physicists still didn’t know whether gravitational waves carried energy or not. That was a big question that had everyone confused. That is, until the GR1 conference at Chapel Hill of 1957, when Richard Feynman convinced most of the audience with the “sticky bead argument.” Among the audience was Joseph Weber. Weber made Aluminum cylinder antennas to detect the waves, and others improved on his design. Then in 1974, 20 years after Einstein died, proof of the existence of gravitational waves was discovered by two astrophysicists, indirectly: a binary pulsar, which showed that gravitational energy was being radiated by an accelerated mass. After 8 years of observation, scientists found that Einstein precisely predicted the rate of the coalescence. Since then, others have confirmed the existence of gravitational waves, also using indirect means. It’s very difficult to measure the waves because their effect on matter is almost negligible, and not all waves are equal. There are four types of gravitational waves: Stochastic, Continuous, Inspiral, and Burst. Stochastic waves originate from the early universe. They are small and pass by mixed together at random. Continuous waves form from imperfections in the spin of a massive object, like a neutron star. While the spin is constant, the wave’s frequency and altitude also remain unchanged. Compact Binary Inspiral waves originate as pairs of massive and dense objects (such as two neutron stars, two black holes, or a neutron star and a black hole) inspiral. Burst waves originate from short-duration or unanticipated sources. Very little is known about them. After it was found that Weber’s antennas weren’t working, Rainer Weiss started building an interferometer prototype. Invented by Albert Michelson, this device uses multiple sources of light to create an interference pattern in order to make very small measurements. What followed were years of prototypes, funding requests, design improvements, and The Blue Book, which lead to the development of the engineering marvels GEO600, Virgo, and LIGO, all of which collaborate to enhance their search. KAGRA, in Japan, is currently in development. A space-based interferometer was canceled, but one may be developed in the future. All this lead up to roughly 3 years ago, when at 4:50 am local time, on September 14th, 2015, LIGO sensed gravitational waves of a merger of two black holes through direct physical contact. After several months, after it was determined to be real, the discovery was announced at a press conference in February of 2016, giving rise to a new era of astronomy, one where Einstein may be proven wrong. The universe is now more transparent to us than it has ever been before.
Now, onto gravity waves.
Gravity waves form when air parcels, imagine a cubic foot of air, are oscillated by buoyancy and gravity in an otherwise flat fluid flow in a surface between layers of different densities in a planetary environment. This can happen for a variety of reasons, such as wind traveling over mountains. These waves then affect atmospheric tides in the stratosphere and mesosphere, and weather in the troposphere as they propagate vertically and horizontally, carrying momentum and energy with them. To observe gravity waves, meteorologists use pressure sensors, imaging data, and techniques such as hodograph analysis. In the troposphere, thin cloud and sky bands are signs of the waves, whereas in the stratosphere moving bands of atmospheric airglow, spectra from chemiluminescence of atmospheric molecules, are used. Therefore, gravity waves are physically induced. Other atmospheric waves are thermally induced; the result of temperature and density contrasts.
TL;dl: Gravity waves are ripples in the atmosphere, whereas gravitational waves are ripples in the space-time fabric.