Just to be clear, there are 2 Birth Registrations at play here:
WILLIAMS, WILLIAM (Mother's Maiden Surname:) JOHNS
GRO Reference: 1876 J Quarter in REDRUTH Volume 05C Page 263
JOHNS, WILLIAM HENRY WILLIAMS (Mother's Maiden Surname:) -
GRO Reference: 1876 J Quarter in HELSTON Volume 05C Page 221