There’s a bit more complexity here to explore as there isn’t a straightforward answer.
Jung created what we now call “cognitive functions” upon which the MBTI is based. Jung was never against MBTI, but there are many accounts demonstrating this wasn’t how he intended the personality type which is why he avoided to endorse or reject the MBTI. He was in general against any framework that told people what they are at the cost of finding out for themselves.
Each person leads with their dominant function. The inferior function is the opposite of the dominant function. In mbti terms, if I’m an ENFJ, my dominant function is extroverted feeling and my inferior one is therefore introverted thinking.
Before I move on I need to explain animus and anima. Animus is the “masculine” counter type in a female and anima is the feminine counter type in a male. There is a significant overlap between anima and shadow.
Now, Jung believed that our anima/animus shows up as our inferior function. Things might be getting a bit complicated here so to over simplify it I would say that he intended the inferior function to represent our internal, unconscious opposite. So my animus would be male because I am female, and it would take on an introverted thinking appearance - for example in dreams or projecting it onto other people.
John Beebe is a famous jungian analyst who came up with the concept of shadow functions. He extended the original 4 functions to 8. In Beebe’s work, the shadow functions are the opposite of the conscious functions. Remember that here we’re talking about cognitive functions not MBTI functions.
So if we go back to my ENFJ example, my cognitive functions are FeNiSeTi, so my shadow functions would be FiNeSiTe. The MBTI equivalent would be INFP. The shadow side of an ENFJ is an INFP - but a shadow INFP will never manifest in the same way as a real INFP because shadow is an unhealthy expression.
Now if we go to the concept of Shadow as Jung intended it, shadow represents anything we repress, suppress or deny from our conscious awareness. If for example my boss embarrasses me at work I will actively try to suppress that memory because I don’t want to deal with the internal humiliation. When we do this, we put that experience into the unconscious in the shadow. Over time the unattended shadow grows and grows, until it starts seeping through our experience. Jung said that whatever we reject in ourselves we project on others. So if I reject anger in myself, I will project onto others that they are angrier than they are, or I will get extremely (disproportionately) triggered when someone is angry.
There are definitely connections between the two but the answer isn’t completely straightforward. Beebe suggested that aspects of our (jungian) shadow will show up in dreams as characters who have that specific dominant function. So for example the opposite of Fe (dom) we have Fi, then part of my shadow will show up as a character with introverted feeling. We can then start to recognise shadow aspects in dreams by noticing what dominant functions these characters have.
I made a video about shadow so if you want to learn more about it, check out the video (or the transcript) in this blog post.