Yeah, I've run into this problem as well, bummer that it was during your defense! Everything turn out oke?

In a sentence, the general linear model is just the standard linear model form as we all know it Y=AX+E (Where X is the design matrix and A a matrix of parameters ) used in many procedures: ANOVA, ANCOVA ect and fit with OLS (with all normal assumptions). But in generalized linear modeling, the key difference is a relaxation of the OLS; i.e. the errors do not need to follow a normal distribution, but may follow any error model of your choice.

I totally agree with you that the names are not very useful. Lets think of some better names and start a trend, by stubbornly refusing to use the old names