I found several options for our tour in southern part of Latin America (Patagonia, Lake District), but all of them mention "hotels and hostels". What does it really mean ? Are hostels going to be like dormitories ? Is it always advertised like that for Latin America tours, or I am just looking at very cheap tour operators ?

If you are looking at English language websites, hostels usually means shared dorms, although a lot of them are now offering private rooms with or without private bathroom. In Spanish an "hostal" with an a is often similar to a B&B, a hostelry rather than a hostel..

I found "hosteria" used often in Patagonia and usually meant small hotel with private bath, but not shared rooms or bathrooms.

Hostería can refer to somewhere with rooms but can also mean just somewhere to eat in the countryside.

If they give the names and location of any of the lodging, why not post it on here so we can see to what sort of lodging they are referring?

Yes ask for the names. If this includes Torres del Paine you could very well be staying in lodging with shared bathrooms.