Yes, it compares full time jobs but the difference in pay is driven by the difference in those jobs, not the gender of the people in them.
i.e. if there were only 2 jobs, engineer and teacher, and all men became engineers and all women became teachers then the gender pay-gap would be the difference between what engineers were paid on average vs what teachers were paid on average.
This incorrect slicing of data and reaching an incorrect conclusion is played out in crime statistics with race as well, anything where there is some predominant identifier that is useful to someone for political reasons becomes the way to slice the data and assumed to be the root cause of whatever disparity is then found, often ignoring other more significant factors.
With the pay gap, it's down to the overlap between gender and the tendency for women to not pursue the STEM fields which are ultimately higher paying. Throw in shorter working periods, leaving to have children etc... and you quickly get a nice juicy headline, ripe for misuse.
Putting women down as earning nothing when taking care of children I guess shouldn't impact things too much because it's median income but it does seem to ignore that aspect and also that many women are more likely to work in part time positions (I'm guessing).
That Obama's own administration produced the report and put the warning on the first page shows to me that he intentionally used it knowing it to be wrong. Thus feeding the narrative of oppression and unfairness that divides people, hopefully so Clinton could get those women voters. Cynical politicking.
Women are done a disservice with this crap because nothing can change due to simple economics. What would be better and more likely to benefit women is to decide, as a society, that we should put greater value on the softer sciences like teaching and nursing and pay them accordingly. e.g. invest in the "Singapore" method of teaching.