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Tropical modes of variability, including the Madden‐Julian Oscillation (MJO) and the El Niño‐Southern Oscillation (ENSO), are challenging to represent in climate models. Previous studies suggest their fundamental dependence on zonal asymmetry, but such dependence is rarely addressed with fully coupled ocean dynamics. This study fills the gap by using fully coupled, idealized Community Earth System Model (CESM) and comparing two nominally ocean‐covered configurations with and without a meridional boundary. For the MJO‐like intraseasonal mode, its separation from equatorial Kelvin waves and the eastward propagation of its convective and dynamic signals depend on the zonal gradient of the mean state. For the ENSO‐like interannual mode, in the absence of the ocean's meridional boundary, a circum‐equatorial dominant mode emerges with distinct ocean dynamics. The interpretation of the dependence of these modes on zonal asymmetry is relevant to their representation in realistic climate models. Plain Language Summary: In Earth's tropical regions, recurring patterns—such as El Niño and atmospheric waves that come with storm clusters—have a large influence on the global weather and climate. These patterns are also challenging to represent in modern climate models. Previous studies suggest that the behavior of these patterns depends on the east‐west contrast in the Pacific ocean, but these studies typically focus on the atmosphere while ignoring relevant actions in the ocean, or vice versa. In this study, we address the question by using a state‐of‐the‐art climate model with a full‐blown atmosphere and ocean. We compare two designs with simplified continental shapes, one with east‐west contrast and the other without. The behavior of atmospheric waves is more realistic with an east‐west contrast. On the other hand, in a global ocean with no land blocking the east‐west direction and therefore no east‐west contrast, phenomena similar to El Niño can still occur around the equator, but with different ocean processes. Understanding the essential conditions for these patterns will contribute to better climate models for prediction, helping with the preparation for and mitigation of extreme weather and climate events. Key Points: Two idealized coupled models, with and without a meridional ocean boundary, show Madden‐Julian Oscillation (MJO)‐ and El Niño‐Southern Oscillation (ENSO)‐relevant modes of tropical variabilityZonal asymmetry affects the distinction of an MJO‐like intraseasonal mode from equatorial Kelvin wavesWithout the ocean's meridional boundary and the associated ENSO‐type dynamics, an interannual mode still persists around the equator [ABSTRACT FROM AUTHOR]