Univariate models and multiple regression (regardless of whether you use GLM, logistic, linear regression etc) will commonly generate different results. Variables that are signficant in one won't be in another. It is because univariate analysis just looks at the explained variance in the DV by the single variable. In multivariate models only the variance explained by that IV which is unique (that is not shared with any other independent variable) is used to calculate effect size and thus signficance. When various IV predict parts of the same variance in the DV, and commonly they will, the results will be very different than with just a single variable predicting the DV.