One of the big issues when it comes to English speakers and the Holy Roman Empire is that we translate two words as 'Imperial' that have different meanings in German. We tend to translate both Reichs- and Kaiserliche- as 'Imperial', when--in German--the former refers more to the institutions and idea of the realm/empire, whereas the latter focuses more on the personhood of the Emperor. So, when something is called 'the Imperial Army', it can either mean 'the Army of the Empire' or 'the Army of the Emperor'. This can lead to confusion in the Early Modern period, espescially when we're dealing with politicking in the Holy Roman Empire. However, as I understand it, convention is to call the army fighting for the Emperor--whoever that may be--gets to be called 'the Imperial Army', regardless of where it came from. Hopefully, this should answer your question. Simply being called 'the Imperial'--or as I often see it, the Imperialist Army--does not imply it was an army of the Holy Roman Empire, but rather could just be saying that it was the army fighting for the Emperor.

However, to go into more depth, another concern is that armies did not tend to draw exclusively on one group. A Scotsman might very well find himself fighting for the Emperor against the French, even though his King is supporting the French against the Emperor.^1 So, almost all armies would consist of troops drawn from around Europe, even though they might pre-dominantly consist of recruits from one area or another. We tend to call these 'the Spanish Army' or the 'French Army' based off who they're fighting for, rather than where the troops came from. Charles V's army no doubt includes Germans, but also likely consisted of a great deal of Spaniards, Flemish, Italians, and other peoples from across his realm.

A better question to ask if we're wondering whether the army is the army of the Empire or the Emperor is: "Who is paying for the war?" Is the army being paid for out of the Emperor's treasury, through his own incomes, or is it an army voted for and paid for by the Reichstag and Imperial Estates? Unfortunately, I don't know that information about the army Charles V brought with him to Italy, so I can't answer you there, but hopefully I would have helped you out somewhat with this issue.

1: This is a hypotheticaal situation, not a statement about the Scottish king's position vis a vis the Italian Wars.

Not to be a pedant, but I believe you mean the 16th century (1500-1600) as the two rulers in question ruled then.

It's a little tricky to answer but my interpretation, is that the only army in continental Europe at the time which could truly be considered an 'imperial army' or an army directly linked to the state would be the Ottoman Army, with its large contingent of Janissary corps always ready for active military service.

Wars in the 16th Century, as Geoffrey Parker demonstrated, were fought with foreign mercenaries for the most part, but usually with some leadership and high command from the native country. For example, at the Battle of Pavia in 1525, the whole empire of Charles V was used to draw in soldiers and commanders, with the army led by a man from modern-day Belgium and the Garrison of Pavia led by a Spaniard. Henry Kamen states that the army itself had no clear national origin. Some 50% were German, 30% Spanish and the rest from all over Europe.

Furthermore, land and vassals in the Empire of the 16th century would have provided the emperor with little troops, but probably some money via taxation and loans. This was spent, along with all the new world gold, on mercenaries.

At no point in the history of the Holy Roman Emperor was their a standing army of the kind which would be familiar today. Until the 15th century, it would have been drawn as you say, from vassals and the king's lands, but fairly early on in that century, such troops were entirely ineffective against professional mercenary types which rich emperors could make use of.