The distinction between 'professional' and 'mercenary' is a troublesome on in the Middle Ages, not only for contemporaries and modern historians. Knights, men-at-arms, and other soldiers often fought for pay (stipendiaries), plunder, or through tenure, and often a combination of the three. The payment for waging war caused much tension within the thought of ecclesiastical intellectuals torn between the sins of taking payment to kill and the preventing of rapine through payment (in part solved by the development of Augustinian Just War theory by scholastics and most famously that of St Thomas Aquinas). In 2008, a publication of proceedings at a Swansea conference attempted to address the issue, Kelly DeVries' article is of particular interest and due to the cost of the book I'll quote it liberally instead:

‘Feudalism’ as a word establishing a pattern of socio-economic hierarchy during the Middle Ages has taken a beating lately. Many have questioned its usefulness and accuracy, however by and large their criticism has been directed towards the defining of the lord- peasant relationship and not any military obligation between lords and lesser lords, although there is no doubt that this was a major if not the main component of early feudalism paradigms. Nor has Philippe Contamine’s name change to ‘feudo-vassalic system’ helped here, despite his more focused effort in directing it at the problems of military obligation and recruitment.

Still, for medieval military leaders there was ‘obligation,’ without a doubt, but for most of the common troops in the middle ages soldiering was an occupation not an obligation. Of course, written evidence for this is hard to come by, with most medieval common soldiers unable or disinclined to write about their military experiences, although there are one or two examples, such as Guillaume Guiart’s Branche des royaux lignages, written when the author had become a cleric later in his life but recalling his experiences fighting in the French army against the Flemish rebels of 1302–1305.

But other evidence makes up for the lack of written sources. For instance, excavated graves at the battlefields of Visby (1361) and Towton (1461) have shown that men stayed in or returned to military service when needed—sometimes many years after their earlier fighting experiences—as proven by healed combat wounds on several of the skeletons. The most dramatic of these was to a Towton soldier estimated to have been as old as fifty at the time of his death. He had suffered an incredibly disfiguring sword slash to his face more than 20 or 30 years previously, when he likely fought with the English forces in France. Others had healed wounds in the limbs and even the head but had returned to soldiering. Were these simply men who were trying to regain the adventure and adrenaline-rush of battle? Not likely. They were soldiers by occupation, and that occupation, even if it was only for subsistence, was better than that of a farmer or laborer. If it did bring greater economic rewards—pay and possibly booty or ransom during war, possibly castle guard or garrison duty during peace—all the better. (Of course, they might also gain employment as mercenaries.)

But did regular employment as a soldier make him a stipendiary or a mercenary, and was there a difference? Probably not to the soldier. Take, for example, a hypothetical twelfth-century Flemish soldier listed as a stipendiary in the documents of the time when he is fighting for the Count of Flanders. If he or his unit takes employment as soldiers in England fighting for Henry II, does he then know that he is a mercenary? Or if he is hired to fight in Italy for Frederick Barbarossa is he now a Brabançon?

Medieval levies existed in theory, but were rarely effectively or success- fully called, such as in 1300, when Edward I called his already fatigued feudal levy to military service, only forty knights and 366 sergeants responded. With such a small number Edward was unable to fight his war that year. Problems also arose over whom to call up. Peasants and urban militias were often quite numerous but lacked the skills or discipline to make them effective warriors. There was also some hesitation to take soldiers from either the agricultural or tax-paying sector of society. So militias were almost always mustered for defensive purposes only. An example of this can be found in some documents I recently translated and commented on in the Journal of Medieval Military History. Following the failure of Duke Philip the Good’s Burgundian army to capture Calais in July 1436, urban and rural militias were mustered throughout the southern Low Countries to protect their lands from the anticipated English military response. This came in the form of raids by Humphrey, Duke of Gloucester, and the presence of English ships off the coast of Flanders. Many militia members were called and stood watch outside their towns and villages for the month of August. But where were the professional troops, such as those from Ghent and Bruges who were justly blamed for Philip’s failure at Calais? They were with the Burgundian army that had been withdrawn to Burgundy. They were professional soldiers—although bad ones, letting their inter-Flemish rivalry determine their military activities outside of Flanders. They were not militia. In addition, where there were obligation requirements to combine land holdings in providing military service, such as in the Carolingian Empire and Anglo-Saxon Wessex, these only compelled the service of soldiers and not the land-holders.

Finally, it should be pointed out that while it is true that most early medieval mercenaries are not known for their special skill in a single weapon, at the end of the Middle Ages this becomes more frequent. Genoese crossbowmen are perhaps the most well-known of these sol- diers because of their role in the French defeat at the Battle of Crécy in 1346—although reflecting on my earlier point these were not all Genoese—but English longbowmen, Burgundian handgunners, and German or Hungarian gunners are also mentioned in the sources. All were paid, and paid well—handgunners in the Burgundian army of the mid-fifteenth century were paid the same as a heavy cavalryman. These would give way to the late fifteenth-/early-sixteenth-century landsknechts, well-paid Swiss and German mercenaries, who were, of course, not all Swiss and German.

The recruitment of medieval soldiers and their motivation for fighting are the issues at hand in this article, not just the definition of medieval ‘mercenary.’ Good soldiers were always needed to fill the ranks of medieval armies, and they were always paid, whether by subsistence, wages, booty, rank, status, or nobility. Soldiering was their occupation. And if they could push their pay higher, why should they not be Huns, Saxons, Varangians, Flemings, Brabançons, Catalan, Genoese, or Swiss, even if they were not Huns, Saxons, Varangians, Flemings, Brabançons, Catalan, Genoese, or Swiss?

Kelly DeVries, 'Medieval Mercenaries: Methodology, Definitions, and Problems', in Mercenaries and Paid Men: The Mercenary Identity in the Middle Ages, ed. John France, pp.43-60, (Boston and Leiden, 2008), 54-56.

On the latter part of your question, is a problem DeVries is lamenting and fortunately there have been movements towards removing it. I just recommended to another enquirer The Soldier in the Later Medieval England, (Oxford, 2013) and do so to you too. This is far more affordable than the above book and a thoroughly worthwhile investment.