We aim to better understand the emission of molecular tracers of the diffuse and dense gas in giant molecular clouds and the influence that metallicity, optical extinction, density, far-UV field, and star formation rate have on these tracers. Using the IRAM 30m telescope, we detected HCN, HCO^+^, ^12^CO, and ^13^CO in six GMCs along the major axis of M33 at a resolution of ~114pc and out to a radial distance of 3.4kpc. Optical, far-infrared, and submillimeter data from Herschel and other observatories complement these observations. To interpret the observed molecular line emission, we created two grids of models of photon-dominated regions, one for solar and one for M33-type subsolar metallicity. The observed HCO^+^/HCN line ratios range between 1.1 and 2.5. Similarly high ratios have been observed in the Large Magellanic Cloud. The HCN/CO ratio varies between 0.4% and 2.9% in the disk of M33. The ^12^CO/^13^CO line ratio varies between 9 and 15 similar to variations found in the diffuse gas and the centers of GMCs of the Milky Way. Stacking of all spectra allowed HNC and C_2_H to be detected. The resulting HCO^+^/HNC and HCN/HNC ratios of ~8 and 6, respectively, lie at the high end of ratios observed in a large set of (ultra-)luminous infrared galaxies. HCN abundances are lower in the subsolar metallicity PDR models, while HCO^+^ abundances are enhanced. For HCN this effect is more pronounced at low optical extinctions. The observed HCO^+^/HCN and HCN/CO line ratios are naturally explained by subsolar PDR models of low optical extinctions between 3 and 10mag and of moderate densities of n=3x10^3^-3x10^4^cm^-3^, while the FUV field strength only has a small effect on the modeled line ratios. The line ratios are almost equally well reproduced by the solar-metallicity models, indicating that variations in metallicity only play a minor role in influencing these line ratios.