Yes it seems to be just like a term that they grabbed but perhaps does not really apply.
Indeed, whereas the Reformation also includes Lutheranism, Anglicanism, and the Moravians (Unitas Fratrum), which is quite a diverse group, Reformed mainly refers to classically Calvinist churches. I sometimes see Calvinist Baptists, or Particular Baptists as they were often called, use the term, for example, in the context of the SBC, where there exists both quasi-Arminian and semi-Calvinists (the main difference being that most Baptists subscribe to a memorialist interpretation of Baptism and the Eucharist, or Lord’s Supper as they prefer to call it, whereas most Calvinists and by extension most people who call themselves Reformed follow John Calvin’s sacramental theology which among other things includes a belief that our Lord is spiritually, but not physically, present in the Eucharist).
That said, I believe I have on occasion seen people with Zwinglian sacramental theology, which proposes the sacraments are signs that point to our salvation and to grace, identify as Reformed, since after all, that was the initial doctrine in Greece. The Waldensians of course became Reformed completely, which obscures what we know about their original theology; there is a Waldensian Church in the US in the Carolinas, I think, called the Waldensian Presbyterian Church USA, whose congregation includes a great many of Waldensian descent. Nowadays in Europe the Waldensian name is attached to that of the main Protestant church in Italy, which is basically Methodist. The reason why I include them is because it shows that Reformed covers a diverse ground even if we exclude Protestant churches which are not styled as Reformed.
Then, of those Protestants, you have a group called the Magisterial Reformers, who partially overlap with the Reformed, insofar as they inevitably include John Calvin in addition to Martin Luther, Philip Melancthon, Thomas Cranmer, Saints Jan Hus and Jerome of Prague (venerated as martyrs by the Eastern Orthodox of Czechia and Slovakia) and sometimes Huldrych Zwingli and John Wesley.
Then there is a more extreme group that wanted more intense reforms, which included Anabaptists, Baptists and Puritans, among others, known as the Radical Reformation. Luther was extremely hostile to this group. During the Wars of Religion, these churches, and the Moravians, experienced persecution, which helped drive the population of the early United States, and in England, after a brief anomaly where the Non-Conformists, as they were known, were in charge under Thomas Cranmer; this gap aside, the Non Conformists would regain civil liberties in the 18th century, followed by Non-Trinitarians and to a degree, Roman Catholics, although anti-Catholicism is still a component of the British Constitution unless a change was made I overlooked when they switched from male primogeniture to first-born regardless of gender inheritance, insofar as the monarch and any heirs are disqualified if they convert to Roman Catholicism due to their status as Supreme Governor of the Church of England.
Now, just as Zwinglianism arguably fits between the Magisterial Reformers and the Radical Reformation, the Restoration applies to some churches which predate the overall Restoration movement, but which believed they were restoring the practices of the Early Church, for example, the Quakers. Restorationist movements of the Restorationist era would include the Millerites and the Stone/Campbell Movement, although the former was not the first Sabbatarian church and the latter was not the first church to have a pietistic organization. Indeed, the largest Stone/Campbell church, the Christian Church/Disciples of Christ, is considered mainline Protestant. Another Restorationist group is the Plymouth Brethren, of whom John Nelson Darby is the most famous theologian, having developed the concept of the Rapture and much of the premillenial pretribulation futurism.
