I read somewhere, a year or two ago, that many stradiots in French service might well have been ‘archers’ told off from service with the Gendarmes to serve that purpose - a precursor to the ‘cheveaux-leger’ type. As said by others in this thread, the term seems to have been fairly generic.
Also, when it came to standards, mercenaries often took up a standard provided by their employer (e.g. France, Venice, etc.) when they were raised/contracted and oaths were sworn to serve under them. For example, one large contingent of Landsknechts raised for France carried flags bearing the white cross (of France) on various fields of mixed black and red (stripes, quarters, etc.).
On the 'different flags for different contingents' front might I also offer this: From the the very start of my Italian Wars collection I decided that all units should be able to carry ANY flag. I came up with this (which I think bears relaying at every opportunity):
http://olicanalad.blogspot.com/2010/07/top-tip-flags.htmlThis simple idea allows me to field several armies using the same figures. Here, for example, some Swiss pikemen are being utilised as French Picard pikemen - I just changed their flags.