The atmospheric pressure-temperature profiles for transiting giant planets cross a range of chemical transitions. Here we show that the particular shape of these irradiated profiles for warm giant planets below 1300 K lead to striking differences in the behavior of non-equilibrium chemistry compared to brown dwarfs of similar temperatures. Our particular focus is H$_2$O, CO, CH$_4$, CO$_2$, and NH$_3$ in Jupiter- and Neptune-class planets. We show the cooling history of a planet, which depends most significantly on planetary mass and age, can have a dominant effect on abundances in the visible atmosphere, often swamping trends one might expect based on Teq alone. The onset of detectable CH$_4$ in spectra can be delayed to lower Teq for some planets compared to equilibrium, or pushed to higher Teq. The detectability of NH$_3$ is typically enhanced compared to equilibrium expectations, which is opposite to the brown dwarf case. We find that both CH$_4$ and NH$_3$ can become detectable at around the same Teq (at Teq values that vary with mass and metallicity) whereas these onset temperatures are widely spaced for brown dwarfs. We suggest observational strategies to search for atmospheric trends and stress that non-equilibrium chemistry and clouds can serve as probes of atmospheric physics. As examples of atmospheric complexity, we assess three Neptune-class planets GJ 436b, GJ 3470b, and WASP-107, all around Teq=700 K. Tidal heating due to eccentricity damping in all three planets heats the deep atmosphere by thousands of degrees, and may explain the absence of CH$_4$ in these cool atmospheres. Atmospheric abundances must be interpreted in the context of physical characteristics of the planet.
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