I see the term "Anabaptist" and "Baptist" being used quite a bit. Both believe in not baptizing your babies. But what is the difference between them? There seems to be some distinction.
Understood sociologically, both are Christian groups who separated from their respective parent groups due to their shared denial of sacramental efficacy (including that of infant baptismal regeneration), an idea originated from one of the three key reformation leaders, Huldrych Zwingli. Zwingli later performed infant baptism again (although only as a sign) due to his reaction against the Anabaptists (see Mark E. Moore's 2018 article Zwingli on Baptism).
There are multiple theories of their origins, so this answer will pick theories that seem most likely: one theory for Anabaptists and one theory for Baptists.
This movement started earlier than Baptists, with the Swiss Brethren in 1525, who were dissatisfied with Zwingli. Soon after, they were persecuted by Roman Catholics, Magisterial Protestants (Lutheran and Calvinist state churches), and even by Zwingli himself (!) since they were too radical, earning the label Radical Reformation. One Reformation historian succinctly said (in caricature) that when the early reformers saw the Anabaptists who refused infant baptism they became so upset that they agreed to postpone their fights with the Roman Catholics until they "finished off the Anabaptists".
The name Anabaptist, meaning "one who baptizes again", was the name given to them by their persecutors, who sometimes executed them by drowning (third baptism). Thus they self-identified under different names, but now that the name loses much of its negative connotations, some of them self-identify as Anabaptists. Since they were persecuted by state churches, unsurprisingly, Anabaptists were more conscious of religious persecution and were much more suspicious of governments than were the Baptists.
Over time, Anabaptists acquired more identifying features that separated them from today's Baptists, such as: separation from government (i.e., state churches), being pacifists, being more counter-cultural (more separation/nonconformity to the world), assigning more importance to "good works" (obedience to Sermon on the Mount) in salvation, and being more influenced by Biblical literalism.
Today's groups include the Mennonites, Quakers, Amish, and Hutterites.
One major theory is the English separatist view, which started whenJohn Smyth who, along with other believers who held the same biblical positions (including adult baptism), fled England in 1607 to join Thomas Helwys in Amsterdam and start congregations there. Four years later, they produced the earliest Baptist confession of faith. Roger Williams and John Clarke started the first Baptist churches in America around 1638. Those churches then separated from the Church of England and received protection from the government in Rhode Island. Their theology was more along the lines of Calvinists (Regular Baptist). Later, some (Free Will Baptists) adopted Arminian theology and their denominations were called General Baptists, while the Calvinist denominations were called Particular Baptists.