Not being flippant, that's the difference. graphviz/dot is general-purpose and can be configured to produce UML-like diagrams, but that's labor intensive.
PlantUML takes text and produces UML diagrams from it. It's configurable... as long as you want UML. If you want something else, reach for graphviz.
In my own work, I use dot/graphviz for diagramming abstract syntax trees, while I've used PlantUML a couple times to diagram the layout of structs and to map the high-level relationships between modules in large software projects.
org-mode does a very nice job of integrating both of those formats into documents, fyi.
Putting the emphasis on UML is a bit misleading actually (even though it is literally in the name of the tool). I use it for basically any kind of ad hoc diagramming. Essentially, an equivalent of Markdown for PowerPoint charts if that makes sense. A few quick lines in text that look mostly like what they come out as in the diagram and you have a very nice representation of a workflow etc.
