The meanings are related. Platitudes are banal statements.. One obvious difference is that "banal" is an adjective; "platitude" is a noun. Thus, "it was a banal speech" ("banal" being an adjective that tells us what kind of speech it was). "The speech was full of platitudes." Platitudes are remarks made in the speech. "Banal" just means boring, unoriginal, obvious, trite. A "platitude" is a specific remark or phrase or sentence, which is delivered as if it were a piece of wisdom, but is actually something boring, obvious, and often a stock phrase that people say all the time. Here is an example of a banal speech: "Ladies and gentlemen, thank you for coming out in this inclement weather. The clouds may sprinkle us with rain, but they cannot dampen our spirits. In a few moments, we will unveil this statue, a suitable tribute to the chairman of the Board of Selectmen who has served our town so well for so long. But first, I have the great pleasure to introduce one of the finest people I have ever had the pleasure of working with, State Representative Joan McCarthy, a silver lining in our cloudy day, to say a few words." The whole speech is banal. "The clouds may sprinkle us with rain, but they cannot dampen our spirits" is a platitude.

Its a relatively big difference. Banal is an adjective and means VERY ordinary or boring or unoriginal. For example, you may have a banal conversation where you discuss what you bought at the supermarket or how the traffic is always bad in Beijing. You can also say something like- "Oh I find this painting terribly banal, his earlier work was much better" A platitude is a noun. It is something that is very unoriginal and that we say a lot, so much so that it almost loses meaning. Examples of platitudes are- "Don't worry, I'm sure it'll get better", "Good things come to those who wait", "Forgive and forget", "Everything happens for a reason", etc.