Context. The eFEDS survey is a proof-of-concept mini-survey designed to demonstrate the survey science capabilities of SRG/eROSITA. It covers an area of 140 deg² where ~540 galaxy clusters have been detected out to a redshift of 1.3. The eFEDS field is partly embedded in the Hyper Suprime-Cam Subaru Strategic Program (HSC-SSP) S19A data release, which covers ~510 deg², containing approximately 36 million galaxies. This galaxy catalogue has been used to construct a sample of ~180 shear-selected galaxy clusters. The common area to both surveys covers about 90 deg², making it an ideal region to study galaxy clusters selected in different ways. Aims. The aim of this work is to investigate the effects of selection methods in the galaxy cluster detection by comparing the X-ray selected, eFEDS, and the shear-selected, HSC-SSP S19A, galaxy cluster samples. There are 25 shear-selected clusters in the eFEDS fooprint. Methods. The relation between X-ray bolometric luminosity and weak-lensing mass is investigated (L_bol - M relation), comparing this relation derived from a shear-selected cluster sample to the relation obtained from an X-ray selected sample. Moreover, the dynamical state of the shear-selected clusters is investigated and compared to the X-ray selected sample using X-ray morphological parameters and galaxy distribution. Results. The normalisation of the L_bol – M relation of the X-ray selected and shear-selected samples is consistent within 1σ-. Moreover, the dynamical state and merger fraction of the shear-selected clusters is not different from the X-ray selected ones. Four shear-selected clusters are undetected in X-rays. A close inspection reveals that one is the result of projection effects, while the other three have an X-ray flux below the ultimate eROSITA detection limit. Finally, 43% of the shear-selected clusters lie in superclusters. Conclusions. Our results indicate that the scaling relation between X-ray bolometric luminosity and true cluster mass of the shear-selected cluster sample is consistent with the eFEDS sample. There is no significant population of X-ray underluminous clusters, indicating that X-ray selected cluster samples are complete and can be used as an accurate cosmological probe.