Hello, there.
I'll try to explain in short.
MozTrust - is WHO links to you. DA - is how MANY link to you = popularity. TrustFlow of Majestic is very similar to MozTrust, but since it's two different companies and two different algorithms - here you get the difference in result.
Now, why these metrics don't match the SERPS. SERPS depend on many things - far not just DA or Trust. Mainly is on keywords. So, if you have very specific service/product and you are trying to rank for whole bunch of longtail keyphrases, but at the same time dont have any links - you will still rank in top 20 for whatever many phrases.
Example: you can make any website rank for "super awesome blue and red cat sitting on a stainless steel shelf" and so on. So, if you have whole bunch of pages, optimized for such keyphrases - you will be ranking in top 20 for whole bunch of keywords. However, it doesn't mean whatsoever that you are not spammer (therefore Trust metric will be low) and you can have vurtially no links (therefore low DA).
And the reverse way. If you have high DA/Trust, but trying to rank for very competitive phrase - you won't be able to (or at least the chances are low).
Additionally, high DA doesn't always go with high Trust, it's much better after Penguin update, but still, if Google hasn't caught you as spammer, you'll have high DA, but since the links are coming from low trust websites - your trust metric will be low.
Hope this make sense and helps.