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While most studies on bubble dynamics are carried out in unconfined geometries, less attention has been paid to investigate confined bubbles and wall effects. This paper numerically investigates interaction and coalescence of two buoyancy-driven inline bubbles in a confined cylindrical vessel to study wall effects. An improved volume-of-fluid method is adopted, and high mesh resolution is achieved by dynamic adaptive mesh refinement. The confinement ratio, CR (the ratio of the radius of the cylindrical tube to the radius of the bubble), is introduced to quantitatively describe the wall proximity. In this paper, the interaction between bubbles is divided into three regimes according to the strength of the liquid influx behind the trailing bubble during bubble interaction (i.e., “weak interaction,” “intermediate interaction,” and “strong interaction”). If the CR is larger than a critical value (CR = 4 in this study), the wall effect can be neglected. It is found that wall proximity reduces the strength of the liquid influx behind the trailing bubble, which causes regime transition. In “strong interaction” and “intermediate interaction” regimes, if the CR is below another critical value, which is termed the second critical CR, “strong interaction” is degraded to “intermediate interaction,” and “intermediate interaction” can be degraded to “weak interaction.” A broader range of parameters is studied to explore the effect of confinement on bubble coalescence, and we further discovered that decreasing the CR does not necessarily postpone coalescence. This work provides insights into bubble motion and interaction influenced by the side wall.