What do these two movements disagree on? Also what are the differences in the way each group seeks to study and understand the Bible?
Although the Pentecostal movement originated from Wesleyans (an infant baptism movement) these days the large majority of Pentecostal churches are adult or believers' baptism, and is it reasonable to say that Pentecostalism is a sub-branch of the Baptist movement.
(My guess is that they shifted to believers' baptism because of their strong focus on being baptised by the Spirit, which fits much more naturally in the baptism is a human response camp than the baptism is a sacrament for infants who can't express their own thoughts camp.)
So, that said, I think there are a few major Pentecostal distinctives:
Pentecostals believe in a distinct Baptism with the Holy Spirit. Although they believe all Christians do have the Spirit, at some time after their conversion they have a distinct experience of receiving and being empowered by the Spirit. Spiritual gifts are thought to really be given after this Baptism of the Spirit, and many think that the moment of this Baptism is marked by everyone speaking in tongues.
Non-Pentecostal Baptists would say there is no evidence in the Bible of two classes of Christians like this, and they would also say that the idea that everyone should exhibit the same gift (such as speaking in tongues) is against the Bible.
Pentecostals are continuationists - they believe that all spirit gifts are still given now, including the more miraculous or 'signs' gifts such as speaking in tongues, healing and prophecy. Some Baptists are also continuationists, but in general Pentecostals have a greater expectation that these miraculous things will be experienced to a level that is almost commonplace.
Many Pentecostal Christians teach that the gift of prophecy still continues and is common today. Many things are identified as 'prophecy' by different Christians, but for some Pentecostals this will include new messages given for specific people in specific situations with no doubt whatsoever that it is from God, rather than a wise application of part of the Bible. In the worst cases this can get dangerously close to superseding the Bible, with some saying that their prophecies should be considered to be as definite as inspired scripture and that they cannot be questioned.
What are the main differences between the baptist and Pentecostal traditions?
The main difference would be in how the spiritual gifts described in the New Testament operate today. There are three main views.
- Spiritual gifts were for the early church and none of them operate today.
- Some spiritual gifts still operate today.
- All spiritual gifts operate today just as they did in the early church.
Baptists would tend to hold to either number one or two. Pentecostals would generally tend to hold to number three.
There is a lot of doctrinal variability within both Baptist and Pentecostal churches and you might find all sorts of examples where various doctrines align or oppose each other. For example, dispensationalism and covenantalism might be in alignment or in opposition.