What does "a free bird thinks of another breeze" mean?

In Maya Angelou's poem "Caged Bird," the speaker contrasts the imprisonment and suffering of the eponymous caged bird with the freedom and independence of a free bird.
The given quotation,"The free bird thinks of another breeze," has two meanings. Firstly, it refers back to the first stanza, where the free bird is described as flying "on the back of the wind." The wind here symbolizes the freedom of the free bird. Thus, the "breeze" mentioned in the given quotation also symbolizes the free bird's freedom, and the fact that the breeze is "another" breeze implies just how much freedom the free bird enjoys.
The second meaning of the given quotation is tied up with a second meaning of the word "another." The word "another" can also mean "different," and so the line might also be read as, "The free bird thinks of a different breeze." The last lines of the previous, second stanza, are, "for the caged bird / sings of freedom." As we have already established, the "freedom" here is synonymous with the wind, so the "different" breeze could simply refer to the different kind of freedom that the free bird thinks of relative to the caged bird. The caged bird's freedom, or "breeze," is only an imagined, hoped-for freedom, while the free bird's "breeze" is a very real and thus different freedom, which it perhaps takes for granted.