Context. The study of molecular line emission is crucial to unveil the kinematics and the physical conditions of gas in star-forming regions. We use data from the ALMAGAL survey, which provides an unprecedentedly large statistical sample of high-mass star-forming clumps that helps us to remove bias and reduce noise (e.g., due to source peculiarities, selection, or environmental effects) to determine how well individual molecular species trace continuum emission. Aims. Our aim is to quantify whether individual molecular transitions can be used reliably to derive the physical properties of the bulk of the H2 gas, by considering morphological correlations in their overall integrated molecular line emission with the cold dust. We selected transitions of H2CO, CH3OH, DCN, HC3N, CH3CN, CH3OCHO, SO, and SiO and compared them with the 1.38 mm dust continuum emission at different spatial scales in the ALMAGAL sample. We included two transitions of H2CO to understand whether the validity of the results depends on the excitation condition of the selected transition of a molecular species. The ALMAGAL project observed more than 1000 candidate high-mass star-forming clumps in ALMA band 6 at a spatial resolution down to 1000 au. We analyzed a total of 1013 targets that cover all evolutionary stages of the high-mass star formation process and different conditions of clump fragmentation. Methods. For the first time, we used the method called histogram of oriented gradients (HOG) as implemented in the tool astroHOG on a large statistical sample to compare the morphology of integrated line emission with maps of the 1.38 mm dust continuum emission. For each clump, we defined two masks: the first mask covered the extended more diffuse continuum emission, and the second smaller mask that only contained the compact sources. We selected these two masks to study whether and how the correlation among the selected molecules changes with the spatial scale of the emission, from extended more diffuse gas in the clumps to denser gas in compact fragments (cores). Moreover, we calculated the Spearman correlation coefficient and compared it with our astroHOG results. Results. Only H2CO, CH3OH, and SO of the molecular species we analyzed show emission on spatial scales that are comparable with the diffuse 1.38 mm dust continuum emission. However, according the HOG method, the median correlation of the emission of each of these species with the continuum is only ~24─29%. In comparison with the dusty dense fragments, these molecular species still have low correlation values that are below 45% on average. The weak morphological correlation suggests that these molecular lines likely trace the clump medium or outer layers around dense fragments on average (in some cases, this might be due to optical depth effects) or also trace the inner parts of outflows at this scale. On the other hand DCN, HC3N, CH3CN3 and CH3OCHO are well correlated with the dense dust fragments at above 60%. The lowest correlation is seen with SiO for the extended continuum emission and for compact sources. Moreover, unlike other outflow tracers, in a large fraction of the sources, SiO does not cover the area of the extended continuum emission well. This and the results of the astroHOG analysis reveal that SiO and SO do not trace the same gas, in contrast to what was previously thought. From the comparison of the results of the HOG method and the Spearman correlation coefficient, the HOG method gives much more reliable results than the intensity-based coefficient when the level of similarity of the emission morphology is estimated.
