Dog having issues with other dogs

About 2 months ago I adopted a sweet staffy dog from the shelter and she has been doing good so far but we have had some incidents with other dogs that I am trying to understand. They estimate she is just around a year old and it seems she was not really socialized at all before I got her. I immediately put her in training because she was growling and lunging at people in my apartment building but that has kind of gone away but yesterday I had a training session and the trainer brought out his dog to see how she would do and we spent about an hour just doing heel work and working on getting her to focus less on the other dog even when it was near to her. At the end the trainer was feeling confident and we had them meet- my dog on a leash and his dog just e-collar. I dropped the tension on the leash and my dog immediately went for the other dogs neck- didn’t seem to actually get a bite in as we couldn’t find any bite marks or blood on the other dogs neck but it was hard to get her off of him she was so attached but eventually we did and she got a good bite in her head from the other dog trying to get her off.

This really ruined my confidence in her but the trainer is confident she can get over this. I am just curious if anybody else has any experience with this and any insight? Does she just not know how to play? Does she just need way way way more socialization? There was no growling or barking or any of that sort and it seemed like she wanted to play but clearly I am not a professional or a behaviorist.

There was also another incident of an off leash dog (golden retriever) approaching her while we were playing fetch on a 15 foot leash and he came at her playfully but in a kinda aggressive and scary way kinda pouncing and barking and she bit him in the neck before I could get them separated. Minimal bite but still the other dog was shook up.

Working on muzzle training of course but I am just so scared she’ll never be able to be around other dogs.

Thanks in advance.

Edit- to be clear my end goal is neutrality and I do not except this dog or breed to be friendly with dogs. I was just freaked out by the fact that she immediately went for the neck twice even if both times were minimal damage. And in the trainers defense we did parallel line walks with the other dog with the distance slowly decreasing for the hour and the heel work with the other dog nearby. Trying to stay below threshold.