This is a very good question! Thank you for submitting it.

The answer is slightly more complicated than an outright yes or no. The Habsburg dynasty were primarily based in Austria, as the emperors of the Holy Roman Empire. However, the Austrian Habsburgs had land in the lowlands (modern Belgium and the Netherlands), as well as Hungary. However, there were Spanish Habsburgs as well, who, as members of the same family, ruled Castile and Aragon, which later became Spain. One of these Spanish Habsburgs, Charles V, would become Holy Roman Emperor.

To say that the Holy Roman Empire and the Habsburg Empire were one and the same is not really fair to say. The Habsburg dynasty passed from one generation to the next, with the firstborn son carrying his parent’s title(s). However, the role of Holy Roman Emperor was actually an elected position. Several states in the Empire, such as Brandenburg (later Prussia) and Bohemia (which later fell directly under Habsburg ownership), would elect the emperor. Habsburgs, however, were elected as emperor of the HRE every single election except one between 1440 and the empire’s dissolution in 1806.

Now, you may wonder, if Habsburgs were continually emperor of the HRE, then isn’t the HRE part of the Habsburg empire? The answer to that is: not really. The HRE was not a single state so much as an organization of multiple states, following a basic universal law code and in a shared congress. It was very decentralized, which is why Austrian Habsburgs expanded into Hungary, but the Holy Roman Empire itself did not assist them in doing that. Brandenburg did the same thing, expanding into Prussia without the rest of the Holy Roman Empire being involved. It became the Kingdom of Prussia without the rest of the Holy Roman Empire joining in on its attacks on Poland. There was lots of autonomy in the HRE, so while the Habsburgs were the Emperor, there was only so much that they could control in their imperial states. The Thirty Years’ War is a prominent example of the Habsburgs conflicting with their imperial nations over the religious rights of the states versus the emperor.

The Habsburg dynasty held Austria, Hungary, Spain, the lowlands, and Bohemia, at certain points in history. The Holy Roman Empire included Austria, much of modern Germany, the lowlands, portions of modern Poland, Switzerland, and northern Italy during the specific time you’d like to look at (1570s).

The HRE’s most prominent nations were Brandenburg (Prussia), Austria, Trier, Mainz, Saxony, the Palatinate, Hanover, Bohemia, Bavaria, and Milan, although there were hundreds of individual states.

Spain and France largely shared their beliefs in catholic customs.

TL;DR: The HRE and Habsburg dynasty (empire) were two separate things, the Habsburgs nearly always ruled both the HRE since 1440 and the Habsburg dynasty since its existence, both included a myriad of states, and Spain and France by and large retained their Catholicism.