Context. The dissipation process responsible for the long gamma-ray burst (GRB) prompt emission and the kind of dynamics that drives the release of energy as a function of time are still key open issues. We recently found that the distribution of the number of peaks per GRB is described by a mixture of two exponentials, suggesting the existence of two behaviours that turn up as peak-rich and peak-poor time profiles. Aims. Our aims are to study the distribution of the number of peaks per GRB of the entire catalogue of about 3000 GRBs observed by the Fermi Gamma-ray Burst Monitor (GBM) and to make a comparison with previous results obtained from other catalogues. Methods. We identified GRB peaks using the MEPSA code and modelled the resulting distribution following the same procedure that was adopted in the previous analogous investigation. Results. We confirm that only a mixture of two exponentials can model the distribution satisfactorily, with model parameters that fully agree with those found from previous analyses. In particular, we confirm that (21 ± 4)% of the observed GRBs are peak-rich (8 ± 1 peaks per GRB on average), while the remaining 80% are peak-poor (2.12 ± 0.10 peaks per GRB on average). Conclusions. We confirm the existence of two different components, peak-poor and peak-rich GRBs, that make up the observed GRB populations. Together with previous analogous results from other GRB catalogues, these results provide compelling evidence that GRB prompt emission is governed by two distinct regimes.