Bernal (ABA stacking order) and rhombohedral (ABC) trilayer graphene (3LG) are characterized by Raman spectroscopy. From a systematic experimental and theoretical analysis of the Raman modes in both of these 3LGs, we show that the G band, G' (2D) band, and the intermediate-frequency combination modes of 3LGs are sensitive to the stacking order of 3LG. The phonon wavevector q, that gives the double resonance Raman spectra is larger in ABC than ABA, which is the reason why we get the different Raman frequencies and their spectral widths for ABA and ABC 3LG. The weak electron-phonon interaction in ABC-stacked 3LG and the localized strain at the boundary between ABC- and ABA-stacked domains are clearly reflected by the softening of the G mode and the G' mode, respectively.