In general, طبيب sounds more idiomatic in Standard Arabic if we're referring to a physician, but in many dialects, "doktoor" is more commonly heard. So we could think of "doktoor" as informal, and "6abiib" as formal.
My impression is that tabib is a medical doctor, while دُكتور can be any type of doctor (including a medical doctor)
Your impression is right. And it is better to use طبيب when you are talking specifically about a medical doctor, that's a better sound Arabic. It is related to the word طِبّ which is medicine.
Sorry if this question does not fit to this particular lesson, but this is the first time I can make it to the forum since last lesson. Why does the "little w" in tayyid have a slash below it? I get that that's the symbol to make consonants geminate, but I thought the slash over a consonant made it be followed by an "a", so I thought it should be pronounced "tayyad"
Great question! In contemporary Arabic convention, the little slashes (called faati7ah ["opener"] an kasrah ["brokenness"], for the slash over and below respectively) come over and below the little w (shaddah ["pull"]), rather than over or below the letter itself. Quranic writing conserves an earlier tradition where the slashes behave like you would expect though. So طيِّب ("kind" [of a person], "good" [of a smell or taste]) is pronounced "6ayyib" and طيَّب ("he disinfected" [of a wound]) is pronounced "6ayyab."