People around the world make a big mistake: they are excited about English sound symbols and think they are learning the IPA. But in fact, they are not.
Take the English /t/ as an example. There are at least three ways to say it: 1) as in <sent>, with little aspiration (puff of air), 2) as in <tree>, with an almost ch sound, and 3) as in <city> if spoken in General American accent, with the tongue quickly tapping the area behind the upper teeth.
So with one single sound /t/, there are at least three ways of actually saying it: [tʰ],[t͡ʃ] or [ɾ].
If what you are learning is only at the /t/ level, or the phonemic level, you are not learning the IPA. Because the IPA cares about the actual ways of saying the sounds, or the phonetic level.
That’s exactly why the IPA stands for International PHONETIC Alphabet.
In General British English, the DRESS vowel as in words like <text>, <men>, and <best> has long been given the symbol /e/. It was true when the symbol was created, but now what people actually say is [ɛ] in the IPA, i.e. with a more open jaw. To put it in another way, if /e/ was really IPA, what people say would have been something with a much closer jaw.
Another example is /r/. If that was really the IPA, people should be saying English words like <road>, <bring>, and <run> with the Italian or Spanish trilled r as in words like <gracie> ‘thank you’ and <terre> ‘land’.
Most English dictionaries, therefore, are indeed using an adapted version of the IPA, instead of the actual IPA. If they (or your pronunciation teacher) claim they are teaching the IPA, there are only two possible reasons: 1) They don’t know what they are doing or 2) They are interested in what’s inside your deep pocket.
