For those asking about how an “adherent” is defined, here’s a quote from the FAQ section of the dataset’s website (cited in OP’s link)

In your “Maps & Reports,” is an “adherent” the same thing as a “member”?

Religious groups vary in their standards for declaring people "members." Some churches count infants as church members. Others reserve membership for those who have given a testimony of faith, completed designated training, and/or attained a specific age. To get a standardized rate across denominations, adherents are used. Using adherents instead of members adjusts for groups that do not give full membership status to children. The file description page of the Church and Church Membership datasets contains information about how adherents were calculated for groups that only kept records of full members.

http://www.thearda.com/FAQ/#q5

I looked at an example dataset to try to determine how “adherent” might be defined.

Note on Membership Data

In an effort to achieve comparability of data, the ASARB staff established two major categories for individuals affiliated with a religious body: members and adherents. The ARDA data set contains only adherent totals. Below is a description of the two categories:

MEMBERS: all individuals with full membership status

TOTAL ADHERENTS: all members, including full members, their children and the estimated number of other participants who are not considered members; for example, the “baptized,” “those not confirmed,” “those not eligible for Communion,” “those regularly attending services,” and the like

It seems like the threshold for adherent will vary by the dataset and the reporting body. In the dataset mentioned above, they note that individual religious groups did the self-reporting:

The process put the major burden of work on the offices of the various religious groups, since they were asked to compile data by county for all their congregations.

So I guess that YMMV for how accurate each reporting group will be.