The James Webb Space Telescope (JWST) recently measured the transmission spectrum of K2-18b, a habitable-zone sub-Neptune exoplanet, detecting CH4 and CO2 in its atmosphere. The discovery paper argued the data are best explained by a habitable “Hycean” world, consisting of a relatively thin H2-dominated atmosphere overlying a liquid water ocean. Here, we use photochemical and climate models to simulate K2-18b as both a Hycean planet and a gas-rich mini-Neptune with no defined surface. We find that a lifeless Hycean world is hard to reconcile with the JWST observations because photochemistry only supports <1 part-per-million CH4 in such an atmosphere while the data suggest about ∼1% of the gas is present. Sustaining percent-level CH4 on a Hycean K2-18b may require the presence of a methane-producing biosphere, similar to microbial life on Earth ∼3 billion years ago. On the other hand, we predict that a gas-rich mini-Neptune with 100× solar metallicity should have 4% CH4 and nearly 0.1% CO2, which are compatible with the JWST data. The CH4 and CO2 are produced thermochemically in the deep atmosphere and mixed upward to the low pressures sensitive to transmission spectroscopy. The model predicts H2O, NH3, and CO abundances broadly consistent with the nondetections. Given the additional obstacles to maintaining a stable temperate climate on Hycean worlds due to H2 escape and potential supercriticality at depth, we favor the mini-Neptune interpretation because of its relative simplicity and because it does not need a biosphere or other unknown source of methane to explain the data.