na-adjective
administrative; businesslike; practical
Describes a manner, attitude, or process that is efficient, matter-of-fact, and focused on getting things done without unnecessary emotion or decoration.
彼の事務的な対応は、かえって信頼できると感じた。
His businesslike response actually felt trustworthy.
会議は事務的に
The meeting proceeded in a practical manner and finished in 30 minutes.
na-adjective
impersonal; perfunctory; mechanical
Often carries a negative nuance of being cold, detached, or lacking human warmth; used when someone acts like a robot or goes through the motions without genuine feeling.
店員の事務的な「いらっしゃいませ」にがっかりした。
I was disappointed by the clerk's perfunctory 'irasshaimase'.
彼女の手紙はあまりに事務的で、友情を感じなかった。
Her letter was so impersonal that I didn't feel any friendship.
そっけない means brusque or curt in a way that feels unfriendly. 事務的 can be neutral or negative, but implies a systematic, office-like detachment rather than simple rudeness.
Compound of 事務 (じむ, 'office work, business') + 的 (てき, '-like, -ish'). The meaning follows naturally from the components.