one parent
Refers to a single parent in contrast to both parents (二親). Often used in contexts like 片親の家庭 (single-parent household).
See also: 二親 (ふたおや)
He grew up in a single-parent household.
single parent
Specifically denotes a parent raising a child alone. Overlaps with sense 1 but emphasizes the parent's role.
As a single parent, balancing work and childcare is tough.
cheap multipack sweet bread rolls (stereotypically associated with low-income single-parent households)
Compound of 片 (one side, single) and 親 (parent).