CD: Crossdressing/crossdresser. Wearing opposte-sex clothing. Can be as innocent as teenage boys wearing girls' jeans, or dykes sporting mens' shirts. I'd say it used to be used more often back when society itself was a lot more gender-binary (male and female rigidly defined) and other terms hadn't come about. It's a common expression of androgyny (a blending of both gender qualities.) They may or may not try to 'present' or 'pass' as the sex whose clothing they're wearing.
For example, a drag queen or king (man dressing as a woman, or a woman dressing as a man) is a type of cross dresser, though usually it's for theatrical purposes. A drag queen may or may not be a gay man (usually is) but it doesn't mean that they actually want to transition to woman.
Transgender is a broad umbrella for anyone who doesn't feel like the sex they're born as meets their gender. Could be someone considering transition, someone who's gender fluid (shifts between masculine and feminine personality), someone who's genderqueer (above gender/both genders/neither) or gender->-bleeped-<- (typically ostentatious gender conflicts. Ex: A friend of mine who would wear a cami and skirt with a hairy chest and full beard.)
Transsexual is typically reserved for when you actually acquire cross-sex characteristics, such as growing breasts (Male to female, or MTF) or the lengthening and engorging of the clitoris (female to male, or FTM.) Or a full on penile inversion sexual reassignment surgery (or SRS, turning the penis into a vagina.) Hormones and surgeries cause this.
Some people are born Intersexed, the modern term for hermaphrodite. While transsexuals typically have no clear physical explanation, people who are intersexed have a clear cross-sex physical condition. Such as a male with an ovary, or unusual genital development, a female body with male or mutated chromosomes, etc. I personally feel that being trans intersex of the brain.
Transvestite would be someone crossdressing for sexual purposes. Classically, a straight man who enjoys wearing lingerie for sex, but doesn't want to be a woman and isn't gay.
Labels... categorize and add quick explanation to complicated situations. Sometimes, they help you fit in to an identity when your own identity is so confusing and maligned. But everybody has their own term or label for their own expression (or not.)
