Context. Tentative correlations between the presence of dusty circumstellar debris discs and low-mass planets have recently been presented. In parallel, detailed chemical abundance studies have reported different trends between samples of planet and non-planet hosts. Whether these chemical differences are indeed related to the presence of planets is still strongly debated. Aims. We aim to test whether solar-type stars with debris discs show any chemical peculiarity that could be related to the planet formation process. Methods. We determine in a homogeneous way the metallicity, [Fe/H], and abundances of individual elements of a sample of 251 stars including stars with known debris discs, stars harbouring simultaneously debris discs and planets, stars hosting exclusively planets, and a comparison sample of stars without known discs or planets. High-resolution échelle spectra (R ∼ 57 000) from 2−3 m class telescopes are used. Our methodology includes the calculation of the fundamental stellar parameters (T eff , log g, microturbulent velocity, and metallicity) by applying the iron ionisation and equilibrium conditions to several isolated Fe i and Fe ii lines, as well as individual abundances of C, O, Na, Mg, Al, Si, S, Ca, Sc, Ti, V, Cr, Mn, Co, Ni, Cu, and Zn. Results. No significant differences have been found in metallicity, individual abundances or abundance-condensation temperature trends between stars with debris discs and stars with neither debris nor planets. Stars with debris discs and planets have the same metallicity behaviour as stars hosting planets, and they also show a similar [X/Fe] −T C trend. Different behaviour in the [X/Fe] −T C trends is found between the samples of stars without planets and the samples of planet hosts. In particular, when considering only refractory elements, negative slopes are shown in cool giant planet hosts, whilst positive ones are shown in stars hosting low-mass planets. The statistical significance of the derived slopes is low, however, probably because of the wide range of stellar parameters of our samples. Stars hosting exclusively close-in giant planets behave in a different way, showing higher metallicities and positive [X/Fe] −T C slope. A search for correlations between the [X/Fe] −T C slopes and the stellar properties reveals a moderate but significant correlation with the stellar radius and a weak correlation with the stellar age, which remain even if Galactic chemical evolution effects are considered. No correlation between the [X/Fe] −T C slopes and the disc/planet properties are found. Conclusions. The fact that stars with debris discs and stars with low-mass planets do not show either metal enhancement or a different [X/Fe] −T C trend might indicate a correlation between the presence of debris discs and the presence of low-mass planets. We extend results from previous works based mainly on solar analogues with reported differences in the [X/Fe] −T C trends between planet hosts and non-hosts to a wider range of parameters. However, these differences ...