I hate to confuse anyone even further, but all the previous posters are both right & wrong.
Here's why: Depending on which school of thought you follow as an Urban Planner determines how you will lay out your city.
In antiquity, cities (if they could be called that at all) were built as a function of superstitions and natural processes. They would be closely packed to maximize materials and the like, but laid out based on the belief that some areas were considered either "sick" or "healthy".
Eventually, the "Father of urban planning" Hippodamus of Miletus designed a regular grid city that incorporated public squares and a city center surrounded by government buildings. This design made every street the same width, and typically followed the cardinal points.
More than a millenia later, under the rule of the Napoleon Empire, Paris saw the next major revolution in urban planning. At this time, a hierarchy to streets was developed. "Boulevards" became the major thoroughfares, while "rues" became secondary. The original use of the word "Avenue" was for long parks usually containing national monuments of some sort. These public spaces were flanked by boulevards.
Then, in the early 1960's American planners started using what is called "street heirarchy". This is where most of us (from the US) get our understanding of the relationship between street types and their use. The irony of this design style is that there was very little standardization. However, the popularity of the automobile did bring about certain commonalities. President Eisenhower further defined this style with the implementation of his Interstate project, and lesser known federal code mandating all new streets must allow two adjacent tanks to travel unhindered. The new "Interstates" became the major thoroughfares, followed by "Highways" as the secondary routes, third are "Avenues" or "Boulevards", fourth are "Streets" and finally "Alleys".
So, after my long-winded explanation let me offer a summary. The use of "avenue" vs. "street" are now completely inter-changable. Although, many city planners (in the US) have chosen to name all roads North-South "avenue" and East-West "street" by blending two styles (Hippodamus grid & Street Heirarchy).
Hope this helps end some confusion.