Magnetic skyrmions are nanoscale vortex-like magnetization textures that hold great promise for next-generation memory and spintronic devices. While extensive research has focused on discovering such localized spin textures in bulk magnets and multilayers with heavy metals, there is a growing interest in finding them in two-dimensional (2D) magnetic materials. In this research work, we report two distinct phases of the 2D CrxTey family: non-centrosymmetric CrTe1.38 and centrosymmetric CrTe0.96, with a Curie temperature of around 200 and 300 K, respectively. Detailed magnetic study indicates a prominent out-of-plane magnetic anisotropy in CrTe1.38. In contrast, CrTe0.96 exhibits a weak uniaxial magnetic anisotropy. Lorentz transmission electron microscopy shows that the spontaneous ferromagnetic ground state of CrTe1.38 consists of Néel skyrmions, whereas CrTe0.96 exhibits Bloch domain walls, consistent with their crystalline symmetries. This research expands the quasi-2D CrxTey family and opens up new avenues for exploring non-trivial spin structures and their potential applications in spintronic devices.