Recent advances in thin film technologies enable us to engineer structural details of surface and interface in transition metal oxide films, and provide numerous valuable opportunities to manipulate electric and magnetic properties via strong couplings among charge, spin, and lattice degrees of freedom. In this work, we exploit an optical second harmonic generation technique to determine crystalline symmetries of surface and interface of compressively strained SrRuO3 thin films, which have been widely used as one of representative ferromagnetic metals in oxide devices. We reveal that the structural symmetries of the surface, the inner-bulk part, and the interface of the films are given distinctly owing to the compressive strain and its relaxation. Furthermore, we trace evolutions of the surface/interface structural symmetries with variations of temperature and film thickness, and discuss their similarities and differences compared to the bulk crystal. The structural phase diagram presented here will provide fundamental information of the surface and interface structural symmetry in exploring electronic and magnetic phenomena emerging in relevant oxide heterostructures.