Castration can be done in a variety of ways, chemical, surgical, or physical damage to the testicles. Some also include removal of the penis, without removing the testicles in the definition. It ideally is done under proper medical care by a doctor, but can happen in any other way such as accident, cutters, etc...
Orchiectomy (or Orchidectomy) is specifically and only used to describe the medical procedure for surgical removal of the testicles. It is entirely possible that a person may have other procedures done, but those will have their own separate terms to describe them. (i.e. I had an orchiectomy AND a scrotectomy done as my castration surgery)
I would also add that Eunuch is a gender description, and can be used as a descriptive term under some circumstances (I suggest that it be in medical circles since it may effect things like test results and medical diagnoses) but there is no need to use it as a "presentation" (how does one present as a eunuch anyway

) or generally... I present as male, and answer male on most non-medical surveys and forms....
WheelyFixed
Paraplegic - T-5, ASIA-B. 2010 Injury left non-functional & frustrated. 4/24/22, stop T. 5/4 start 3.75mg Lupron. 6/29 - T ~0. 7/7 - start E. 9/2 stop Lupron. 3/30/23 - GOT LETTERS! surgery (O&S) 9/28/23. Doing 0.1mg/day E patch as HRT