A series of molecular dynamics simulations have been performed at 300 K to investigate the differences between commensurate surface contact interactions of NaCl and TiO2. The contact studies were carried out between two bodies of identical material which consisted of blocks of NaCl probes (with cross-section n x n, where n = 2, 4, 6, 8 and 10 atoms) and blocks of TiO2 probes (with cross-section 2 x m, where m = 4, 5, 6, 7 and 8 unit cells) with NaCl (001) and TiO2 (110) surface slabs, respectively. By studying the vertical force as a function of distance between the probes and surfaces and the corresponding atomic configurations, mechanistic descriptions of the probes' contact with the surfaces and subsequent withdrawal have been obtained. We have observed both a characteristic instability 'jump' involving large atomic displacements and an increase in attractive force in both materials. However, the nature of the jump processes differ in that a more elaborate atomic reorganisation occurs in TiO2 during the jump process, whereas it is essentially a straightforward, commensurate contact for the NaCl system. In addition, the NaCl probes can be withdrawn completely from the surface with no permanent structural change to the probe but with an associated hysteresis at the jump region. Conversely, withdrawal in the TiO2 systems depends on the extent of compression on the probe. At sufficiently high compression, a probe may collapse and subsequently fuse at the contact junction. The withdrawal of the TiO2 probes also shows complex behaviour, whereby the initial creation of a defect hole leads to the formation and subsequent elongation of a necking structure at the lower part of the probe.