Well, to start with tratado
can have other meanings beyond the past participle of tratar. It can be:
1- An official agreement (treaty, like the Treaty of Tordesillas o Tratado de Tordesillas)
El tratado de XXX le daba la mitad del imperio a un rey y la otra mitad a otro.
And official is the keyword there. It is the kind of agreement that you get when the parties involved might be kingdoms, empires, the pope, etc.
2- A book, discussion or work about a certain matter, generally long, extensive and deep (treatise)
El Libro de YYY es el mejor tratado sobre matemáticas escrito en el siglo XIII
Trato
, apart of the variations for Tratar
can mean also an agreement, but is more like a comercial or mundane agreement than the official agreement of Tratado
.
Tengo un trato con mi socio. Él se encarga de las finanzas y yo del papeleo burocrático.
You could even have an informal trato with somebody
Tengo un trato con mi padre. Si saco todo sobresalientes me dejará usar su coche los fines de semana.
Te propongo un trato, si tú barres el suelo yo friego los platos y hagos las camas.
Note that in Spanish we would favor acuerdo for a legal agreement (for example between two companies) instead of trato.
About the difference between trato
and tratamiento
, when referring about addressing to somebody, I think there is no big difference. Maybe just personal preferences to pick one word or the other.
A: Deberías corregir la cabecera de ese email, el tratamiento correcto para esa persona es debería ser "de usted" y no "de tú".
B: En serio? Yo siempre le trato "de tú" cuando le veo!.
That treatment
could also mean medical treatment, in which case is always tratamiento
and never trato
.
El tratamiento para esta enfermedad consiste simplemente en una vacuna.