Here you go.
There are two cuttings of Timothy grass. The first cutting is coarser, lower in protein and offers more chewing time. First cutting Timothy is usually used for race horses and export to the Pacific Rim. The second cutting is brighter in color, softer and much preferred by the retail client due to its color and texture. Often horses eat it much faster (remember, faster is not always better. ) Timothy hay is high in fiber, especially when cut late. It is considered part of standard mix for grass hay and provides quality nutrition for horses."
Where I live, all the hay is cut and baled in the summer months. So first cut usually comes around May/June. But it may be different further down south, depending on where your feed store gets it's hay from. Usually this time of year the hay all comes from where it's been stored for the winter. So the cuts available just depend on what it is they have stored.
I have both cuts as my rabbits have different preferences. The first cut is very thick stems, lots of fiber, but some of my rabbits don't like that, so I also have the second cut which is the timothy with the softer stems and higher protein.