Different p-values for normal regression and interaction terms

while performing a logistic regression for two variables I also wanted to perform an interaction analysis. Particularly, I was looking to the use of a diagnostic test over time (before and after a certain period, a binary variable) and deepending on age (elderly >75 y.o. ore younger individuals, still a binary variable). However, the p-values given in the interaction analysis for the single components are different than the original given by the single analysis, so I would like to understand what are the actual p-values reported in the interaction analysis.

Here the codes and results:

summary(glm(DB$$Test~ DB$$Time,family = binomial(link="logit"))


p-Value 1.52e-06

summary(glm(DB$$Test~ DB$$Age, family = binomial(link="logit"))


p-Value 5.4e-09

summary(glm(DB$$Test~ DB$$Time* DB\$Age,family = binomial(link="logit"))


p-Values:

Time= 7.67e-06

Age= 0.0491

Time:Age= 0.6922

So, where does this 0.049 come from? what is it testing?

When you modify your model by adding or removing predictors, whether main effects or interactions, the coefficient estimates, standard errors and (therefore) $$p$$ values of all the terms already in the model will change. (Except for very exceptional circumstances.) What you are seeing is thus not surprising.