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There are two common Pentecostal doctrines that are at play here:
Firstly the general belief with regard to (water) Baptism is that it is for believers only; this is called credobaptism (or just believer's baptism) and is a belief that almost all Pentecostals hold in common with Baptists. It means that any form of infant baptism (not just Catholic christening) would be regarded as an invalid "baptism". They may also emphasize the form of the baptism as well, with full immersion being required for a valid baptism.
The defining belief of Pentecostals (ie their distinguishing belief from other evangelicals etc; their raison d'etre) is their teaching that the baptism of the Holy Spirit is an important experience in the life of a believer that is subsequent to their regenerative salvation (new birth) and is also distinct from water baptism (although it is possible for them to occur simultaneously); this is also known as the doctrine of subsequence. According to this doctrine, the baptism of the Holy Spirit is received by faith for the purpose of empowerment to witness for Christ (who has already been received as Lord and Saviour) and may occur before (eg household of Cornelius) or after water baptism (eg early Ephesian believers). Pentecostals most commonly believe that the sign of having received the baptism of the Holy Spirit is "speaking in tongues" (a human or heavenly language that has not been learned naturally).
The above applies for the majority of Pentecostal denominations, but a notable exception are Oneness Pentecostals who have some quite disctinct beliefs:
The majority of Pentecostals do not view baptism as essential for salvation, and likewise, most Pentecostals are Trinitarian and use the traditional Trinitarian baptismal formula. However, Oneness Pentecostals view baptism as an essential and necessary part of the salvation experience and, as non-Trinitarians, reject the use of the traditional baptismal formula. - wikipedia/Pentecostalism