Both definitions are correct. The term self is used both ways.
APA and ABA both call lavender "self-blue." It actually meets both definitions: it breeds true and it is one uniform colour.
Extended black (E) meets both definitions also, except that to be completely black additional melanizing genes are also needed. As a dominant gene, if E is present in only one copy and paired with another bird who also carries only one copy of E, about 25% of the offspring will not inherit E from either parent.
Blue is incompletely dominant; while it breeds PREDICTABLY, it does not "breed true" in always giving the same outcome. Splash breeds true. While the various combinations of the blue gene are typically called blue/black/splash, from a technical sense that is not correct. It should be blue/not-blue/splash. Not-blue does not always equate with black.
Lavender (lav) is recessive. It is not a leaky gene; if a bird shows lavender, is carries two copies. A bird with one copy cannot be visually distinguished from one that has no copies. If two lavenders are bred together, the outcome is always lavender.
All of that said, with any of these, other genes carried by each parent bird can combine and give various patterns or additional dilutions or restrictions to the resulting offspring.