In Scrum, a time-boxed daily stand-up with a structured format is mandated by the framework. If you don't have a daily stand-up, you aren't following the core Scrum methodology.
Kanban is less prescriptive, and doesn't actually mandate the daily stand-up as a formal ceremony. However, Kanban teams often borrow the practice from Scrum for the same reason that Scrum teams implement Kanban-style boards: because it's an effective agile practice that promotes a continuous inspect-and-adapt feedback loop.
Status Pulls vs. Stand-Ups
There's a big difference between a status pull and a daily stand-up. A status pull is when members of the team take turns reporting into a central authority (e.g. a line or project manager), while a daily stand-up is a commitment and coordination meeting between the members of a team.
Agile frameworks actively encourage other forms of status tracking and communication about the state of the project, and visible artifacts like the Sprint Backlog or kanban story board greatly reduce the need for formal status pulls. When there is information that can't be gleaned directly from framework artifacts, agile practitioners generally try to gather the necessary information through dialogue and conversations with team members rather than through formal reporting in a group setting.
Status pulls as a form of formal reporting are strongly discouraged in agile methodologies. I would go so far as to say that formal status pulls are inherently a "project smell" that indicates that there is a fundamental process problem with the agile implementation.
Scrum defines a stand-up in a very specific way. The Scrum Guide says, in part:
The Daily Scrum is a 15-minute time-boxed event for the Development Team to synchronize activities and create a plan for the next 24 hours. This is done by inspecting the work since the last Daily Scrum and forecasting the work that could be done before the next one.
Not all agile framework mandate a daily stand-up. Kanban does not, but many Kanban teams still implement stand-ups as a way to foster collaboration and continuous improvement, and as a clearinghouse for issues that might impact flow or cadence.
Regardless of the framework or methodology, a stand-up is intended to provide a mini-planning meeting for the current day's work. The "three questions" typical of a daily stand-up in Scrum or Extreme Programming are just a formula to assist teams in coordinating the day's work by helping everyone quickly identify items that are ready to be handed off, intra-team dependencies, and obstacles to progress.
Any discussion items that don't fit within the time-box or the format of the meeting should be noted and addressed by team members outside of the stand-up. For example, Bob might say that he's unable to embiggen his widget because he's waiting on Alice to ensmallen her doohickey. Alice might respond that she's going to finish the doohickey today and will coordinate with Bob after the meeting, or she might tell him that they need to have a post-standup palaver to discuss the matter further.