責任 and 義務: responsibility and obligation
Compare responsibility for work and outcomes with an obligation to act.
Being responsible for work and outcomes
責任 (せきにん) refers to responsibility for assigned work or its outcomes. 「この仕事には責任があります」 says that this work carries responsibility, without specifying legal conditions.
「責任者に相談してください」 asks someone to consult the person in charge. It does not instruct the person asked to take over all responsibility.
Something required
義務 (ぎむ) means an obligation. 「参加する義務はありません」 says there is no obligation to participate, not that participation is forbidden.
「義務を果たしました」 means fulfilling an obligation. It reports completed action rather than a promise to do it later.
Words versus actual requirements
「責任を持って確認します」 expresses undertaking a check responsibly. 「確認する義務があります」 states an obligation to check. Distinguish the actor's stance from a requirement.
The words themselves do not establish the applicability of a law or contract. This guide concerns meaning and negation scope; actual obligations must be checked in the relevant rules.
Does 「義務ではありません」 mean that it must not be done?
Show the answer and why
No. It says that something is not obligatory, not that it is prohibited.