There are differences between them. “明白” is more perceptual, conceptual, emotional... Well my English is not enough to explain that. For example, you may say "我懂中文" but you can't say "我明白中文", for Chinese is some kind of knowledge. So "懂" has more meanings than "明白". But mostly you can replace "明白" with "懂".

基本上相同。但有時還是不一樣。 懂：比較重"知識性"，如：這一篇文章的每一個字，你都懂嗎？ 只可以當動詞。 明白：跟"說明" "解釋"的事有關，如：我說了這麼多，你還不明白我的意思嗎？ 可以當動詞，也可以當形容詞，跟"清楚"差不多。

是相同的

same meaning, different usage

一样