Rule 176 and Rule 267

Indian Polity Parliamentary Procedures

Context: The Rajya Sabha proceedings were disrupted as members of the Opposition demanded a discussion on the Manipur violence under Rule 267.

According to the Rules of Procedure and Conduct of Business in the Council of States, Rule 267 relates to suspension of rules.
Any member can request, with the Chairman's consent, to temporarily stop following a rule for a motion related to that day's business.
If the motion is carried out, the rule in question will be suspended for the time being.
However, this rule doesn't apply if there's already a specific way to suspend a rule in a particular chapter of the Rules.
Under this rule, Rajya Sabha MPs can give a written notice to suspend all listed business and discuss an issue of importance the country is facing. For instance, if a Bill is to be introduced,it would be listed.But if a rule is coming in the way, 267 is aimed at suspending the rule.

Rule 176 of the Rajya Sabha relates to Short-duration discussion, which is a brief discussion not exceeding two-and-a-half hours.
Any member desirous of raising discussion on a matter of urgent public importance may give notice in writing to the Secretary-General specifying clearly and precisely the matter to be raised.
Provided that the notice shall be accompanied by an explanatory note stating reasons for raising discussion on the matter in question.
Provided further that the notice shall be supported by the signatures of at least two other members.
Once the Chairman admits the notice, the rules say he, in consultation with the Leader of the Council, will fix the date on which such matter may be taken up for discussion and allow such time for discussion.
It means that a short-duration discussion under Rule 176 can be taken up immediately, a few hours later, the next day or can be fixed for a later date and time.
The rule says there shall be no formal motion or voting under a short duration discussion.
Member who has given notice may make a short statement and the Minister shall reply shortly.

Adjournment motion is governed by Rules 56-63 of the Rules of Procedure and Conduct of Business in Lok Sabha.
It is “a motion for an adjournment of the business of the House for the purpose of discussing a definite matter of urgent public importance may be made with the consent of the Speaker”.And the rules say not more than one such motion shall be made at the same sitting.
Along with discussion the adjournment motion has an element of censure.Only Lok Sabha has this privilege because the Rajya Sabha can not bring down a government.