While they may not be the most famous two lines of English poetry, they are certainly frequently discussed and debated. You could ask many well read people about there meaning, and you would get different answers. What it amounts to is to what school of literary criticism the person explicating the lines belongs. Historical, mimetic, post-structural, and etc.
The key words in your opening sentence are "may be." If you asked the average person to quote a couple of lines of poetry, would he or she say "Beauty is truth, truth beauty"? Maybe, if that person is well read or an English literature student. Or maybe he would say, "How do I love thee, let me count the ways" or "Let me not to the marriage of true minds" or even "Roses are red, violets blue." It's all relative!
There is a difference between believing there is something and thinking there is or is not something. When one believes that there "is," but thinks there "is not," it is clear that people can believe IN something, but THINK that it does not exist or never will exist. This is just one very elementary example. The way that I interpret this quotation is that BELIEF encompasses our hopes, dreams, and ideals. THINKING involves our logical and rational side. These two do not mix or mesh sometimes, as we all know.
I am not sure if these two lines are the most famous in English poetry. But I am sure that these are great lines of poetry. The poet supplies the message of the Greek urn--'Beauty is truth, truth beauty'. Consider how the message of equating 'beauty' and 'truth' is made complex by the use of chiasmus that involves a syntactic deviation. The chiasmus indicates the tension, for Keats's intended meaning is never as simple as beauty being equal to truth; there may be a truth which is far from the beautiful.
What follows--'That is all ye know on earth/And all ye need to know'--further adds to the ambivalence of the poem's closing note.Even if we believe that beauty and truth are simply equal or identical, that simplistic equation is the limited knowledge of the ancient work of art. We need to know more; we need to know that even a not-beautiful thing can be true.
"The last two lines of "Ode on a Grecian Urn" may be the most famous in English poetry"...does not stand as an appropriate observation...there are lines which touch us, make us feel,loaded with philosophical deligh, and so on.Keats is a poet of our heart;these lines move us and force us to think the aesthetics of beauty..dimensions of life do not go on parallel ways.They differ in kind and degree;there lies the answer to ur observation.