['drɔɪŋ] [dʒɔɪn] I really can't distinguish them.
Most of the time in most accents, these words should be distinct.
First of all, the vowels are different. Drawing contains the /ɔː/ followed by /ɪ/, while join contains the diphthong /ɔɪ/:
- /ɔɪ/ is a diphthong, a single vowel sound that changes from one place of articulation to another gradually. It cannot be pronounced as two separate sounds.
- /ɔː/ and /ɪ/ are monophthongs, each single vowel sounds which do not change noticeably in place of articulation over time. Although there is often a smooth transition from one to the other, you can pronounce draw and ing separately; you can't do the same with join. And because /ɔː/ and /ɪ/ are separate vowel sounds, in non-rhotic varieties of English, /r/ may be inserted in between (drawring) to separate them; this cannot happen with join.
Even though we write the diphthong /ɔɪ/ with the same two phonetic symbols, that doesn't mean that it's pronounced in the same way as a sequence of those two vowel sounds:
- In American English, /ɔː/ is likely to be a backer vowel than the start of /ɔɪ/.
- In both American and British English, /ɪ/ is likely to be fronter and higher than the end of /ɔɪ/.
- And of course, /ɔː/ in draw is a long vowel.
And in some American English accents, /ɑː/ is used instead of /ɔː/, making the words more distinct.
Since /r/ may be somewhat palatalized in drawing, it may trigger a phenomenon called yod coalescence, where /d/ becomes the affricate /dʒ/, the same sound that's in join. If you hear the non-affricate /d/ it's join rather than drawing, but if you hear the affricate it could be either word. In that case, the following /r/ should help you distinguish them, but it might be difficult to hear the difference some of the time.
In careful speech, the final /n/ in join is different from the /ŋ/ in drawing, but in casual speech /ŋ/ may become /n/, and in connected speech the nasal may assimilate to other places of articulation (for example to /m/ in drawin' boats). So outside of careful speech, these may be distinguishable some of the time, but not all of the time.
When we listen to words, we almost never hear them in isolation. They almost always come in a linguistic context with other words, and these words carry meaning. We automatically use this meaning to determine which words are possible or likely:
Carol's ＿＿＿ a picture.
If you heard someone say this sentence, but you couldn't hear the word I've blanked out at all, would you be able to guess whether the speaker meant to say drawing or join? Only one of the two words makes sense.
In fact, it's rare that both drawing and join will make sense in a sentence. Even if the words sound very similar (which is possible sometimes in some accents in non-careful, connected speech), you can still use context to tell which of the words was intended.