If you’re at a party and you want to start a good ‘ol fashion argument, you can bring up Taxes, religion, states rights or the difference between a 1/2 a 3/4 or a full bathroom.
For every person you ask, you will get a different answer. Everything from, a toilet and a sink is a 1/2 bath. A toilet/sink is a powder room. A toilet/sink/shower is a 3/4 bath. Yudda, yudda , yudda.
Here is what I’ve come up with….
By code, you can not have a toilet without a sink. they go together like peanut butter and jelly.
But you can have a sink by itself.
powder room?
A toilet-sink is a 1/4 bath?
A toilet-sink-tub is 1/2 bath.
A toilet-sink-shower a 1/2 bath.
These two may be confusing. but if you think about it, you can take only a bath OR a shower.
A toilet-sink-tub/shower combination is a 3/4 bath.
With this you can take a shower and a bath. Depending on how dirty you are.
However that still does not do justice to the toilet-sink-tub and a separate shower. Now that sounds like a full bath!
Of course, this is still just a working theory and does not take into consideration the bidet or the advent of the home urinal.