Determination of the bulk metallicity of giant exoplanets is essential in order to constrain their formation and evolution pathways and to compare them to the Solar System. Previous studies inferred an inverse relation between the mass and bulk metallicity. However, these studies used data mostly for planets orbiting FGK stars. The recent discoveries of giant exoplanets around M-dwarf stars present an opportunity to probe whether they follow a mass-metallicity trend that is different from that of their FGK counterparts. Using evolution models, we characterised the interiors of giant exoplanets with reliable mass-radius measurements that orbit FGK and M-dwarf stars. We then inferred the mass-metallicity trends for both populations. We find that the bulk metallicity of giant planets around M stars is overall lower than that of planets around FGK stars. This yields mass-metallicity relations for the two populations with similar slopes but significantly different offsets. The lack of metal-rich giant planets around M dwarfs could explain the difference in the inferred offset and could be a result of different formation conditions. However, there are only 20 successful bulk-metallicity retrievals for the giant planets around M dwarfs, which results in rather large uncertainties. Therefore, it is of great importance to continue detecting these planets with both transit and radial velocities. Additionally, the characterisation of the atmospheres of giant planets around M-stars would further help to constrain their interiors and facilitate investigations of the atmosphere-interior connection. Such investigations will significantly contribute to our understanding of the possible formation pathways of giant planets.