The ability to change shape is essential for the proper functioning of red blood cells (RBCs) within the microvasculature. The shape of RBCs significantly influences blood flow and has been employed in microfluidic lab-on-a-chip devices, serving as a diagnostic biomarker for specific pathologies and enabling the assessment of RBC deformability. While external flow conditions, such as the vessel size and the flow velocity, are known to impact microscale RBC flow, our comprehensive understanding of how their shape-adapting ability is influenced by channel confinement in biomedical applications remains incomplete. This study explores the impact of various rectangular and square channels, each with different confinement and aspect ratios, on the in vitro RBC flow behavior and characteristic shapes. We demonstrate that rectangular microchannels, with a height similar to the RBC diameter in combination with a confinement ratio exceeding 0.9, are required to generate distinctive well-defined croissant and slipper-like RBC shapes. These shapes are characterized by their equilibrium positions in the channel cross section, and we observe a strong elongation of both stable shapes in response to the shear rate across the different channels. Less confined channel configurations lead to the emergence of unstable other shape types that display rich shape dynamics. Our work establishes an experimental framework to understand the influence of channel size on the single-cell flow behavior of RBCs, providing valuable insights for the design of biomicrofluidic single-cell analysis applications.