The IAU definitions of planet and dwarf planet require that a Sun-orbiting body has undergone the rounding process to reach a roughly spherical shape, an achievement known as hydrostatic equilibrium. The same spheroidal shape can be seen from smaller rocky planets like Mars to gas giants like Jupiter.
Any natural Sun-orbiting body that has not reached hydrostatic equilibrium is classified by the IAU as a small Solar System body (SSB). These come in many non-spherical shapes which are lumpy masses accreted haphazardly by in-falling dust and rock; not enough mass falls in to generate the heat needed to complete the rounding. Some SSSBs are just collections of relatively small rocks that are weakly held next to each other by gravity but are not actually fused into a single big bedrock. Some larger SSSBs are nearly round but have not reached hydrostatic equilibrium. The small Solar System body 4 Vesta is large enough to have undergone at least partial planetary differentiation.
Stars like the Sun are also spheroidal due to gravity's effects on their plasma, which is a free-flowing fluid. Ongoing stellar fusion is a much greater source of heat for stars compared to the initial heat released during formation.