What are the differences/similarities between Kanban and Scrum?

Scrum will boost when it runs containing Kanban practices.
Anecdote: Kanban was initially labelled as non-agile by some agile practitioners.

Similarities
Both relate to Lean, with Scrum inception being the isolation of the Lean core developed by Takeuchi and Nonaka (1986) as the origin for further work by Jeff Sutherland and Ken Schwaber, and Kanban development directly related to Toyota Lean practices being the origin for David J. Anderson´s work.

Transparency and iterative and incremental (continuous) delivery exist in both.


Differences
Scrum is a framework while Kanban is a model or methodology. This has direct implications as Scrum should be applied as it is while Kanban is tailored to the environment.

Due to this Scrum is structured and it has its own roles, events and artifatcs (Definition of Done, Sprint Goal and Increment) while Kanban applies no change to the current company roles or processes initially and it relies on small changes (Kaizen) that happen across time, one at a time.

A Sprint is locked after the Sprint Planning, Kanban always accepts new work. Their boards (radiators) are slightly different, Scrum has a "fixed columns" board while Kanban board has flexible number of columns.

Scrum events are timeboxed, most Kanban processes aren't.

Being a framework Scrum doesn't limit Work in Progress, nor focuses on Lead or Cycle time (albeit this happens in mature Scrum teams anyway), this is so as a framework doesn't define specific application of methodologies else an scaffolding only. Kanban does as its focus is steady flow.

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References
Takeuchi, H. and Nonaka, I., (1986). 'The new new product development game'. Harvard Business Review.