What’s the difference between infant baptism and believer’s baptism?
In all forms of Christian baptism, God claims those being baptized, whatever their age or ability to profess their faith, with divine grace. Clearly an infant can do nothing to save himself or herself, but is totally dependent on God's grace, as we all are -- whatever our age.
Most traditions that practice or recognize as valid the baptism only of believers -- those who have professed faith in Jesus Christ for themselves in some public way -- practice baptism not as a means of grace by which God saves and claims us, but rather as a further act of public profession and/or an act of obedience to the command of Christ that his followers be baptized. That is why these "believer's baptism only" traditions generally refer to baptism as an ordinance -- an act ordained or commanded by Christ -- rather than a sacrament. The term sacrament means "an oath" and refers to God's covenant with us (first of all) and ours in response to God's gracious provision of salvation in Jesus Christ.
United Methodists recognize the baptism of "believers only" traditions, provided those traditions baptize people in water in the name of the Father, the Son, and the Holy Spirit as generally understood in historic Christianity. We offer baptism to people of all ages who have not previously received Christian baptism in any form. We do not rebaptize those who have already received Christian baptism in any form. Even when the people being baptized are believing adults and are ready to profess their faith, our first emphasis is upon the gracious action of God who establishes the covenant of baptism with us rather than upon the individual's decision.