What is the difference between 鸡蛋 and 鸟蛋? I am learning Chinese with Rosetta Stone software and it is based on guessing the sense of words by pictures. 

And I can't guess the difference between various types of "eggs".

When I see normal, probably hen's egg, they write

一个鸡蛋

but when I see some other types of eggs, they can write

一个鸟蛋

In these cases eggs are probably from different birds, not hens.

So what is the difference? Only bird genus or something else?
鸡蛋 is a specific term.
鸟蛋 is a general term.

When we know what kind of bird it is, we use a specific term.
Otherwise, we use a general term.

For example, we call the eggs of 鸭 (duck), 鸽子 (dove), or 鹌鹑 (quail) as 鸭蛋, 鸽子蛋, or 鹌鹑蛋.