'Ablutions' or 'morning ablutions' is the generic term for washing, toothbrushing, showering, bathing, toenail cutting, shaving, hairwashing, nose-hair clipping, and the usual bodily functions.
The fact that the sayings are both in the plural emphasises that there is more than one activity being referred to, not just, say, washing.
The OED says of 'ablute' :
b. intr. To wash oneself; to bathe.
1959 C. MacInnes Absolute Beginners 183 I put on some music and abluted, then made two Nescafés.
2002 Derbyshire Life & Countryside Nov. 128/2 I abluted in a staff loo.., observed the female contingent and then rejoined the march in a bloated Pall Mall.
However, colloquially the term is being taken to mean more than just washing as is witnessed by its use by Tom Ford in a Top Gear piece, written in 2017/2018, where he makes it clear that he includes defecation (he includes a 'hygienic' shovel in his equipment) :
I ponder some more on this the next morning while taking care of my morning ablutions away from camp equipped with a hygenic shovel.
The OED makes it clear that 'ablutions' is :
- Frequently humorous (with mock formal tone). The action or an act of washing oneself; personal cleansing; bathing. Now usually in pl.
I take it that the very archaic nature of the expression is being used in humour and also being used euphemistically in that the whole range of bathroom activity is being politely included within a single term.