The planets and moons in the solar system present a unique opportunity for enriching our understanding of Earth. The remarkable diversity of atmospheric compositions, dynamics, and weather patterns requires us to move beyond Earth-centric paradigms and search for more general theories that can explain the similarities and differences between them. In this work, Saturn's moon Titan is chosen as the point of comparison with Earth for its compositional similarity, active hydrological cycle, and distinct atmospheric dynamics. We investigate the governing physics of climate, clouds, and convection on both bodies with the goal of learning general truths that broadly apply to most, if not all, moist planetary atmospheres. We focus, in particular, on the effects of low to high moisture concentration in the atmosphere. First, it is found that Earth's climate is remarkably stable to significant changes in atmospheric moisture content. In Earth-like climate states, the vapor pressure path at the anvil cloud level is fixed due to spectroscopic properties of water vapor. The largest changes in Earth's climate occur at tipping points that involve transitions from multi-layered to single-layered convective clouds. Second, we demonstrate that the height of congestus cloud-top formation in the tropics is driven by a mid-tropospheric decline in the water vapor emissivity in clear-sky regions, which causes clouds to detrain preferentially between 5-6 km. This clear-sky theory of cloud formation is derived from basic assumptions of mass and energy balance and so should generalize well to other locations on Earth or to other planets and different atmospheric compositions. Third, we show that the transition from steady, quasi-equilibrium (QE) precipitation on Earth to non-steady, relaxed oscillator (RO) precipitation on Titan is predicted by the breakdown of a heat engine model of convection with increasing surface temperature and/or atmospheric moisture content. The breakdown of quasi-equilibrium dynamics occurs due to an imbalance between the work performed by the convective heat engine and the heat of condensation released by the convective motions themselves. The heat engine perspective offers a robust point of comparison between the atmospheres of Earth and Titan based on the first and second laws of thermodynamics, which are system invariant. The heat engine model is, in fact, agnostic of the working fluid and the condensing substance and, arguably, is the best framework to explain why dynamical similarities between present day Titan and a much warmer Earth exist.