Will that trust be lost when I have to trap her to bring her in?
I wouldn't say it would be lost, but there may be a long adjusting period if the cat has never been indoors, or even if it has, it will be a new scary environment. Even cats that aren't on the streets can have long adjustment times to a new location. The good news is, that once she's inside you'll be able to spend way more time with her and she'll likely come around to the idea of being petted sooner than she would if left outdoors.
I wouldn't let this stop you at all! It's the correct step in taming her.
Is there a difference between "barn" cat and feral?, we believe that is what she was - barn cat. Please, any encouragement, advice, would be greatly appreciated. I am praying I can get her in!
The way I see it... a barn cat is a cat that is used in and around a barn to hunt mice, that's its meaning it in the purest forum. A lot of people care for their barn cats to different degrees from there. A barn cat should be but all too often is not spayed/neutered and also have an alternative food source, as cats aren't going to live off of mice alone. They can be very friendly cats, running right up to you, they just are not a cat you bring into your home, as they're used as working animals. My uncle has barn cats, they have kibble, they sleep in the large hay bundles inside the barn, they're shut inside the barn at night to avoid wild animals, they're neutered, and one of the two is extremely friendly even to strangers.
A feral cat is born in the wild and has not had any - or very little - contact with humans. They're afraid of people and avoid them, and it takes a great deal of effort to win their trust. Usually months or years, if ever, and even then usually only to the people that have tamed it.
A semi-feral cat is one that used to live with people in some capacity but had become lost/abandoned and had to learn to fend for its self. They are slowly reverting to a feral state, and it can take these cats a long time to warm up to people as well, depending on their past experiences with people and on their length of time outdoors.
I think your cat falls into the last category, she's warmed up to you very quickly for a truly feral cat; 8 months isn't that
long. At one point she was TNR'ed (trapped, neutered, returned) if you go by the eat tipping - but that just means that the people she initially had grown up around her had never spayed her before she ended up on the street and eventually caught.
My cat was somewhat like that, she took a year outdoors until she left me get close enough pet her, she had been spayed in the past (no ear tipping). When I first carried her inside (after a few months of petting her outdoors she was terrified of the entire house, she went wild inside the first time we closed the door on her, like we'd just given her a death sentence or something; she jumped out a broken window! We continued to bring her inside and we opened an old unused dog door that's built into the side of the house from the backyard. At first she'd just run out the dog door when we put her in the house but eventually she started to come inside as well since we'd put her food indoors and shown her where it was. I suppose that back room with the dog door and her food became her 'safe room' for many months. She started coming in on her own just for food but eventually over another year became relaxed in the entire house, she's somewhat aloof to strangers in the home, but not afraid at all. She's the most well rounded cat I've met.