Both Red-Black Trees and B-Trees are balanced search trees that can be used on items that can have a comparison operator defined on them. They allow operations like minimum, maximum, predecessor, successor, insert, and delete, in O(log N) time (with N being the number of elements). Thus, they can be used for implementing a map, priority queue, or index of a database, to name a few examples.
Red-Black Trees are an improvement upon Binary Search Trees. Binary Search Trees use binary trees to perform the named operations, but the depth of the tree is not controlled - so operations can end up taking a lot more time than expected. Red-Black Trees solve this issue by marking all nodes in the tree as red or black, and setting rules of how certain positions between nodes should be processed. Without going into too much detail, this method guarantees that the longest branch isn’t more than twice as long as the shortest branch, so each branch is shorter than 2*log_base2(N).
This is the ideal structure for implementing ordered maps and priority queues. B-Trees branch into K-2K branches (for a given number K) rather than into 2, as is typical for binary trees. Other than that, they behave pretty similarly to a binary search tree. This has the advantage of reducing access operations, which is particularly useful when data is stored on secondary storage or in a remote location. This way, we can request data in larger chunks, and by the time we finish processing a previous request, our new request is ready to be handled. This structure is often used in implementing databases, since they have a lot of secondary storage access.
