One of the problems with Lego for those not familiar with the blocks is the different sizes that are available and how they interrelate.

Over the years and in different countries the Lego company has used different names for the different sized blocks. I'm aware of at least five different sizes. A very small block for building architectural models was discontinued years ago and i've never even seen one of these. Primo, Quatro, Duplo, Lego and to a certain extent Fabuland denote different sizes of the basic blocks. 

Pictured below are the "standard" two by four Lego block, which is the smaller one, and a larger two by four Duplo brick. as you can see the Duplo brick is around four times the size of the Lego brick but clever design allows the blocks to lock together. When you are describing a brick the number wide and number long of the top studs are used to indicate the size.

An overhead shot showing some Lego and Duplo pieces 

Confusingly the Lego company seems to change the terms a bit themselves. All Lego pieces have LEGO moulded onto them somewhere. Usually inside the studs on top of the piece and quite aften another Lego Group logo on the underside. Duplo blocks can have DUPLO or LEGO inside the studs. 

Below we have some PRIMO blocks and a container that the one on the right came from. The container has Lego, Duplo and Primo logos. The brick on the left from another set has LEGO on the top while the one on the right has DUPLO. Go figure.

Primo blocks will lock onto a two by two duplo brick but the single stud on top limits them to engaging with only other Primo blocks. Because they are designed for small children they do not "lock" as well as other Lego bricks. I have only ever come across one of these Primo to Duplo adaptors pictured below.

When you are looking for genuine secondhand products from the Lego Company the moulded logo inside the stud is a crucial indicator. There have apparently been counterfeits over the years as a brick with the logo is worth more than one without.

Inside a stud, in this case a Duplo brick.

In their recent catalogues Lego (Australia) at least have tried to get a bit more information out there. Below is the photo that appears in one of the recent quarterly issues.

Hope that helps