The Baptist tradition originated in England as a Non-Conformist group started by John Smythe in the early 17th century. Smythe taught against infant baptism and had himself re-baptized (he baptized himself). Smythe also believed in rejecting the establishmentarianism of the Church, and that the Church should be a local congregation of free association bounded by covenant. Like other non-Conformists, the Baptists were persecuted in Britain, and would seek refuge in the Americas. The original Baptists, like Smythe, were of a Puritan variety; but they were not welcome in the Puritan colony of Massachusetts. This led a prominent American Baptist, Roger Williams to leave Massachusetts and establish Rhode Island with the promise of religious freedom (the Baptists rejected the idea of a state church or the government telling people what to believe and believed that religious liberty was a guaranteed right of all people, and being a Christian was a matter of free association).
After the American Revolution and the introduction of the US Constitution which promised religious liberty to all, Baptists were a group that grew and began to thrive in the new nation. However, because the Baptist tradition rejected all forms of church hierarchy and believed only in the local church/congregation, there was an explosion of different kinds of Baptists. What defined a Baptist was certain "Baptist distinctives", not a hierarchal ecclesiastical structure, not even necessary shared doctrine (outside of the certain Baptist distinctives, such as a rejection of infant baptism and belief in believer's baptism). As such while the earliest Baptists with their Puritan heritage were usually Reformed in their theology, later Baptists would adopt an Arminian theology, thus "Reformed Baptists" and "Free Will Baptists". Various issues, theological and practical, would create different groupings of Baptist churches.
Because of this, the Baptist tradition has a great deal of diversity, even within associations and conventions (the closest thing Baptists have, historically, to a larger ecclesiastical structure) there is a diversity from congregation to congregation. This has actually led to modern controversies, for exampling, within the Southern Baptist Convention as the leadership of the SBC has attempted to do some top-down measures to reign in congregations; with congregations in turn having dissociated with the SBC. This was one of the major reasons why Jimmy Carter, a life-long Southern Baptist, eventually left the SBC because he believed the SBC had betrayed its foundational Baptist principles. I only bring this up because it is relevant to the historic Baptist tradition, which historically does not care for top-down ecclesiastical structure--emphasizing the total and free autonomy of the local congregation.
Pentecostalism, on the other hand, is usually said to have its origins in the 1906 Azusa Street Revivals. This is, probably, mostly true--but it's more complicated than that. Pentecostalism has its earlier origins in the Wesleyan-Holiness tradition that emerged in the 19th century, the same tradition that gave rise to the Church of the Nazarene (as an example). And even before 1906 there are examples of Pentecostal-like things happening among these earlier Holiness Churches. However Azusa Street was a major and pivotal moment, and it ultimately led to the formation of distinctively "Pentecostal" churches, such as Assemblies of God. Now, given the historic roots of the Pentecostal tradition, there are some superficial similarities between it and the Baptists; for example a rejection of infant baptism stems from the earlier Holiness Movement having diverse views on the subject (even today the Church of the Nazarene believers baptism or infant baptism depends on personal conscience and the sentiments of the congregation). A case can probably be made that the rejection of infant baptism in the Pentecostal tradition has to do with some influence of credobaptists in the early formation of the movement; as there were many credobaptists who joined (most notably, Baptists themselves). And given Pentecostalism's strong emphasis on a personal encounter with the Holy Spirit, then it stands to reason that those who may have come from paedobaptist traditions (or those which practiced both) wouldn't have had much issue with adopting a credobaptist position if the emphasis was on personal repentance, the choice to be baptized, and then to receive baptism with the Holy Spirit with the evidence of speaking in tongues (the latter being one of the chief distinctive doctrines of the Pentecostal tradition).
Which is to say the Baptist and Pentecostal traditions have very different histories, but there are certain superficial and similar things going on due to either some level of direct or indirect influence (Baptist influence on Pentecostalism, and in modern times also Pentecostal influence on Baptists). Both traditions emphasize a personal and individual participation in Christian religion and thus less stress is placed on historic liturgical practice, giving rise to less structured and loose services designed to fit the specific needs each tradition views as important for their communities (also, no doubt, both having been influenced by the Second Great Awakening in this regard).
Some Baptist churches have been influenced by the Pentecostal tradition, as such there are Charismatic Baptists.
But there are distinctive practices and doctrines which define each tradition. Baptists have their Baptist Distinctives, and Pentecostalism's chief distinctive theological position is baptism with the Holy Spirit with evidence of speaking in tongues.
-CryptoLutheran
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