I've been struggling to understand when these technologies are useful from a practical standpoint, and how they are different from each other. Could an expert check my understanding?
Graph databases: These are easier to understand and manage than a relational databases when relationships are complex, inherited, inferred with varying degrees of confidence, and likely to change. Some examples: a user doesn't know how much depth they'll need in a hierarchy; is inferring relationships from social media with varying degrees of confidence in ID resolution, topic resolution, and the strength of a relationship; or doesn't know what kinds of call center data they're going to want to store; all of these can be stored in relational databases, but they will need constant updates. They're also more performative for certain tasks.
Ontologies: These formal and standardized representations of knowledge are used to break down data silos. For instance, let's say a B2B sales company derives revenue from several different lines of business, which take one-time payments, subscriptions, sales of IP, and consulting services. The revenue data is stored in many different databases with lots of idiosyncrasies. An ontology allows the user to define a "customer payment" as anything that "creates or refunds revenue," so that subject matter experts can appropriately label the payments in their databases. Ontologies can be used with either graph databases or relational databases, but the emphasis on class inheritance makes them far easier to implement in a graph database, where the taxonomy of classes can be easily modeled.
Knowledge graph: A knowledge graph is a graph database where language (meaning, the entity and node taxonomies) are governed by an ontology. So in our B2B example, "customer payment" edges have one-time payments, subscription, etc subtypes, and connect "customer" classes to "line of business" classes.
Is that basically correct?