This work presents a large consistent study of molybdenum (Mo) and ruthenium (Ru) abundances in the Milky Way. These two elements are important nucleosynthetic diagnostics. In our sample of 71 Galactic metal-poor field stars, we detect Ru and/or Mo in 52 of these (59 including upper limits). The sample consists of high-resolution, high signal-to-noise spectra covering both dwarfs and giants from [Fe/H] = −0.63 down to −3.16. Thus we provide information on the behaviour of Mo I and Ru I at higher and lower metallicity than is currently known. In this sample we find a wide spread in the Mo and Ru abundances, which is typical of heavy elements. We confirm earlier findings of Mo enhanced stars around [Fe/H] = −1.5 and add ∼15 stars both dwarfs and giants with normal (<0.3 dex) Mo and Ru abundances, as well as more than 15 Mo and Ru enhanced (>0.5 dex) stars to the currently known stellar sample. This indicates that several formation processes, in addition to high entropy winds, can be responsible for the formation of elements like Mo and Ru. We trace the formation processes by comparing Mo and Ru to elements (Sr, Zr, Pd, Ag, Ba, and Eu) with known formation processes. Based on how tight the two elements correlate with each other, we are able to distinguish if they share a common formation process and how important this contribution is to the element abundance. We find clear indications of contributions from several different formation processes, namely the p-process, and the slow (s-), and rapid (r-) neutron-capture processes. From these correlations we find that Mo is a highly convolved element that receives contributions from both the s-process and the p-process and less from the main and weak r-processes, whereas Ru is mainly formed by the weak r-process as is silver. We also compare our absolute elemental stellar abundances to relative isotopic abundances of presolar grains extracted from meteorites. Their isotopic abundances can be directly linked to the formation process (e.g. r-only isotopes) providing a unique comparison between observationally derived abundances and the nuclear formation process. The comparison to abundances in presolar grains shows that the r-/s-process ratios from the presolar grains match the total elemental chemical composition derived from metal-poor halo stars with [Fe/H] around −1.5 to −1.1 dex. This indicates that both grains and stars around and above [Fe/H] = −1.5 are equally (well) mixed and therefore do not support a heterogeneous presolar nebula. An inhomogeneous interstellar medium (ISM) should only be expected at lower metallicities. Our data, combined with the abundance ratios of presolar grains, could indicate that the AGB yields are less efficiently mixed into stars than into presolar grains. Finally, we detect traces of s-process material at [Fe/H] = −1.5, indicating that this process is at work at this and probably at even lower metallicity.