Right well as the diagnosed sufferer of one of these let me attempt to give you an IS 101 course. There are several conditions that are popularly termed intersex.
Funnily enough these do not always correlate with gender identity issues but sometime they can.
The most frequent condition is one of Androgen Insensitivity. This has five grades ranging from the most mild, grade one partial form up to the complete grade five condition.
People suffering from grade one and two (as indeed I do - I am borderline grade two and three) will almost certainly be sterile, but other than that may simply have the appearance of slightly undervirilised males. That is males with perhaps less body and/or facial hair, higher than average unbroken voices, perhaps no Adam's apple, smaller than average or slightly malformed genitalia (I had mild hypospadias), lower sex drives, etc.
At Grade three and four some ambiguity of the genitalia may additionally be observed, and at grade five the person will appear to all intents and purposes as fully female, although sterile and of XY karotype. In all forms of the condition some degree of gynecomastia will be present.
Additionally disorders of the Aromatase metabolism, otherwise known as Aromatase excess syndrome, may lead to some additional degree of feminisation of the body during puberty
The next common condition is Klinefelters syndrome. In this condition an extra X chromosome is present leading to the karotype XXY. In many respects the effects of this can be similar to AIS, but klinefelters suffers are often quite tall and slight in build, and in some cases there may be some mild mental impairment.
There are additionally some other much rarer conditions such as 5 alpha reductase deficiency, Turner syndrome, Swyer Syndrome.
All of the syndrome above affect XY karotypes first and foremost. There are a few conditions which conversely affect mainly females they are CAH Congenital Adrenal Hyperplasia, which can cause ambiguity in female genitalia. PCOS Poly Cystic Ovary Syndrome which is not universally acknowledged as an Intersex condition but which commonly causes elevated testosterone levels.
Finally there are mosaic conditions (also sometimes known as Chimeras). These are essentially the reverse of twins in that they happen when a male fetus and a female fetus fuse in the womb, giving rise to a creature which is in a very real sense part male and part female.
Low free testosterone may be associated with one or more of the conditions. My own testostreone levels were never that high and postoperatively are as close to zero as makes no difference. However as others have said much complex testing is required to establish a diagnosis and in most cases, in my opinion, it is hardly worth the effort.
I hope all of that made sense and is of some help.
There are a number of us in this community who exist in the IS/Trans crossover territory. We are, in essence, no different to anyone else here.