These four terms exist at different levels of a hierarchy, not as four separate, equal categories.

"Sex hormones" (also called gonadal steroid hormones) is the broad category of all steroid hormones involved in reproductive development, sexual characteristics, and reproduction. This umbrella includes three classes: androgens, estrogens, and progestogens (e.g., progesterone). All are synthesized from cholesterol via a shared steroidogenic pathway in the gonads (testes/ovaries) and adrenal cortex.

Androgens are the class of steroid hormones responsible for male-type ("masculinizing") effects: development of male genitalia, spermatogenesis, muscle mass, bone density, deepening of the voice, and body/facial hair. Androgens include testosterone, dihydrotestosterone (DHT), androstenedione, and DHEA. They are produced mainly by the Leydig cells of the testes in men, but also by the ovaries and adrenal cortex in women (in smaller amounts) - as noted in the physiology literature, androgens act in both males and females, just at very different concentrations (testicular production is roughly 7-8 times higher than ovarian production).

Estrogens are the class of steroid hormones responsible for female-type ("feminizing") effects: development of breasts, uterine lining growth, menstrual cycle regulation, and maintenance of bone density. The main estrogens are estradiol (most potent, produced mainly by the ovarian granulosa cells), estrone, and estriol. Estrogens are produced predominantly by the ovaries in women, but also by adipose tissue, the adrenal cortex, and even in men (testosterone is converted to estradiol via the enzyme aromatase).

Testosterone is the single most important and abundant androgen - it is one member of the androgen class, not a separate category. It's produced primarily by Leydig cells in the testes (and in smaller quantities by the ovaries and adrenal glands in women). It can be converted peripherally into:

Both androgens and estrogens are present and biologically active in both sexes, just in different concentrations. In men, a portion of testosterone's effects on bone density are actually mediated through its conversion to estradiol - some evidence suggests estrogen accounts for a larger share of bone-protective (antiresorptive) effects in men than testosterone itself does directly. In women, ovarian and adrenal androgens contribute to libido, muscle, and bone health, and excess androgen production (e.g., in PCOS) causes hirsutism, acne, and menstrual irregularities.

Sources: Medical Physiology (Ch. 54, puberty/gonadal steroidogenesis); Textbook of Family Medicine 9e (Testosterone/Estrogen sections); Berek & Novak's Gynecology; and a supplementary review, Impact of estrogens in males and androgens in females.

If you want, I can go deeper into any one axis - e.g., the biosynthesis pathway from cholesterol to testosterone/estradiol, or the clinical effects of excess/deficiency of each.