If something “depends on” something, then (literally translating) it “hangs from” that thing. A dependency is a necessary condition, so if a depends on b, then b → a (b implies a) in formal logic.
If something “is determined by” something else, then it contains some value which is a result of that thing. If a is determined by b, then b causes a to be something. There could be some default value of a (like the empty set, or 0, or something else) that a has in the absence of b (in which case a is still determined by b, since it’s b’s absence that gives a its value). In that case, a is determined by b, but a does not depend on b- since a can exist with or without b, but a’s value is determined by that of b.