They are both Agile methodologies but…
Kanban doesn’t do sprints as Scrum does. There are no sprints, sprint plannings, sprint retrospection etc… The development is continious, like an assembly line. Constantly new and new task are coming in the backlog, the team members take them, do them and so on…
Both Kanban and Scrum are not so much different nor competing, they can be used together. One such example may be if we generally use Scrum’s sprints, planings, retrospectives, but for the part where we do the task, we may use Kanban. A kind of a hybrid – outside Scrum, inside Kanban.
Using Kanban, you as a developer should only pick a task from the Backlog, put it in Doing state, and once completed – move it in Done.
Kanban is more suitable for continiously improving given product, support, bugfixing etc… while Scrum is more suitable for solving more complex problems, usually during the initial development of the product. So, yet another example where these two methodologies may be used together: while we develop the product and deploy on production, maybe Scrum is more suitable. But later on, if the product is operational and needs bugfixing, pathes, updates (and certanly it will)… maybe Kanban would be better.
One feature of Scrum that I personally find as an advantage over Kanban
In some sence Scrum protects the developers from the constant changes and demands from the clients – lets do this too, lets do that too, change this task for it’s not good and we need smth. else…
By starting a sprint with given set of tasks and given time commitment, you actually say to the client „Look, these are the tasks, and they will be done by… some date… That’s it.“