The word believer has always had the meaning "someone who believes in a god or have a religious faith" as it is the earliest sense of the word. This is the usual sense unless otherwise specified within a context.
Here is the definition of the earliest sense of the noun believer and the earliest citation from OED:
1. Theology. A person who believes in a god or the doctrines of a religion; esp. a Christian. Sometimes: spec. a member, esp. a fellow member, of a particular Christian group.
See also Old Believer n., right believer at right adj. 6c.
a. Without construction.
?a1425 (▸a1415) Lanterne of Liȝt (Harl.) (1917) 5 (MED) Þe feiþ of trewe bileuars.
b. With in, †on; also of or possessive.
1530 G. Joye in tr. M. Bucer Psalter of Dauid f. 215 He promysethe his helpe to ye belevers in him.
Here is the definition of the second sense of believer and the earliest citation of this sense from OED:
2. A person who believes in the truth, accuracy, reliability, genuineness, virtue, value, or efficacy of a thing or person.
a. With in, of or possessive, that.
1596 T. Nashe Haue with you to Saffron-Walden To Rdr. sig. C4v I protest I doo not write against him [sc. Harvey] because I hate him, but that I would confirme and plainly shew to a number of weake beleeuers in my sufficiencie, that I am able to answere him.
b. Without construction.
1646 Sir T. Browne Pseudodoxia Epidemica 115 That a Brock or Badger hath his legs of one side shorter then of the other,..an opinion..received not only by theorists and unexperienced beleevers, but assented unto by most who..behold and hunt them dayly.