Well, jazzo can come and correct me, but a pergola is a flat top structure (almost always) the has upright columns, and cross structures like joists, but no roofing material. I have only seen them made of wood, but they could be made of metal, (i can envision one that way, don't know if they ever have been done, but i see no reason why not!) or stone(real or concrete to look like stone) I don't think brick would work...

it is often adjecent to a house but I have seen them free standing.. Last year, Martha Stewart living had instructions on how to build a free standing one to support a wisteria vine, and very frequently, pergola's are covered with flower or fruiting vines. here in NY, grapes would be most common. a home support for table grapes grown in the back yard.

a gazebo is always a free standing structure, I have never seen one attached to a house or other building.

they are round, or square, or octoganal, and no doubt, also pentigons, or hexigons.. and septigons and many other shapes.
They are covered -- they have roof.. sometimes it is slatted, and not rain-proof, but most often it is a real roof. and 99% of the time, it is a pitched roof, not a flat one. The sides are open or half open or screened in..They are made of wood or cast iron, or stone, or brick. or any other building material, including metal and glass.

Gazebo's have floors too, some times just grade level poured concrete, sometimes fancy brick, sometimes wood decking, but they all have a sense of a 'building'.

Norm Thomas, (of This Old House fame) has build both on TOH shows. pergola's tend to be square/rectangle-ish, some are like covered passages, some as large as parking spaces.. pergola's are about 50/50 for floors, some do, some don't.

I think they are different things, not just different names for almost the same thing a veranda/porch/terrace/covered deck/deck -- each could be very very similar to each other and the words could be used somewhat interchangably, but a pergola and gazebo are different.