Learn English – Do “lettuce” and “let us” have the same pronunciation

English has a lot more vowels than most languages, so most learners need to re-train their ears to recognize the additional vowels. In both British English and American English, the difference between ball and bowl is small, but significant. It is easy for native speakers to recognize because their ears are trained to do so.

In ball, the vowel is a long vowel: that means that it sounds the same all the way through. The same long vowel occurs in law- /lɔː/ in BrE and /lɑː/ in AmE.

In bowl, the vowel is a diphthong, which means that there is a glide between two different sounds. The same diphthong occurs in low- /ləʊ/ in BrE and /loʊ/ in AmE.

You can see the difference clearly in this spectrogram of a British English speaker saying ball and bowl. In the first word, ball, the long vowel is the same all the way through. In the second word, bowl, the diphthong sound changes, starting at the red cursor line.

Regarding your comment about casual, fast-paced conversations: when people speak casually, and when they speak quickly, the parts that lose clarity are the function words: the little words that provide the structure for the language.

Take the word and, for example: the strong form is /ænd/, but most of the time we use the weak form /ənd/. As speech gets progressively faster and/or more casual, it becomes /ən/ and finally /n/.

Meanwhile, the important words- nouns like ball and bowl- are usually stressed, and don't soften up in the same way. The central vowel in a stressed word is about as protected as you can get.

You might get some de-stressing if the noun is preceded by an adjective (the red ball) or when it's part of a compound noun (a furball), and this might weaken the clarity a little, but not, in my opinion, enough to make it impossible to discriminate for a native listener with the same accent.