Some women do ejaculate upon orgasm, but not all. I have ejaculated personally, and if anyone says it is impossible/fake, I will fight them, knock them out, and then ejaculate on them. Well, no, I will try to restrain myself. But yes, it is a contested topic.
The similarity of female ejaculation and peeing lies in that both the ejaculate and urine exit the body through the urethra (as in males, I might add). Some people argue that female ejaculation is a modified form of urine, due to the presence of urea and creatine (the main chemical components of urine) in samples of female ejaculate
[1] [2]. However, these chemicals are present in very small amounts, and as a point of comparison it must be noted that
both are also present in male ejaculate (see 3rd paragraph).
I could go into more detail, but instead I'll refer you to
Wikipedia--see especially parts 2 and 3, and the external links.
As for my personal experience, if this helps, I find that penetration of the vagina is not necessary for female ejaculation. Also I find that my ejaculate varies in consistency at different points in my menstrual cycle. It is generally bad-smelling and sometimes has a tinge of orange for a few days after my period stops. I can't say I have an especially good handle on what it's like during my period, as it generally mixes with the blood, but my highly iffy impression is that it doesn't seem as foul during the beginning of my period as afterwards. Certainly it continues in the usual sweetish, clear state up to when my period begins.
I am NOT a biologist or doctor, but if I had to hazard a guess as to why ejaculate seems to be affected by one's menstrual cycle, I'd guess that the hormonal changes associated with menstruation also have an effect upon the Skene's glands (insofar as they produce female ejaculate). Hormones are basically the driving force behind everything that happens "down there", as I understand it, so it stands to reason that some hormonal changes should be associated with ejaculation as well.