Small functions were defined in complex analysis and next in ultrametric analysis. Order of growth and type of growth were also defined in complex analysis and have a similar definition in ultrametric analysis. We compare these two notions in the same way, in l C and on a complete ultrametric algebraically closed field IK of characteristic 0 such as l C p . The set of small functions with regards to an entire function f is a ring. The set of entire functions with an order of growth strictly inferior to a number t is also a ring. If t is the order of f , it is included in the previous one when f is regular, but not always when f is not. If an entire function h is small with regards to an entire function f , that does not imply that its order of growth is inferior to this of f . All these statements are the same on l C and on IK. Moreover, in IK, we have a specific result: if f is clean and the cotype of f is strictly superior to the cotype of h, while the type of f is less than the type of h, then h is a small function with regards to f .