A problem is basically an error that Funnelback can state with confidence - the WCAG check fails and there are no caveats that might turn the failure into something that can be ignored.
A warning might be an error - lots of the WCAG checks require a human component in making a decision of whether something is actually an error.
eg. An image only requires alternate text if it's conveying meaning. Purely presentational items can omit the alt text. Or a PDF that doesn't validate might pass WCAG by supplying an alternate text version of the same document. Funnelback logs these are warnings.