クライアント is a loanword often used for professional service clients (e.g., lawyers, consultants). 顧客 is broader and more common in retail and general business.
Etymology
Compound of 顧 (こ, 'look back; care for') and 客 (きゃく, 'guest; customer'), literally 'a guest one cares for'. The reading こかく is a rare historical variant.
