Preschool and nursery are exactly the same for 3/4 year olds. The only difference is that traditionally 'preschool' is term time only and 'nursery' is year round, but many nurseries still offer term time only sessions (ours does). The difference is just that preschools don't offer sessions out of term time, so people who have to work tend to go with nurseries. But what they do is exactly the same following the early years curriculum. Each nursery or preschool will vary a bit in what they emphasise just based on how they run.
Ours is more monetsorri style, so there are no separate classrooms. All the kids are together, 9 months to 4 years, though they might do different things throughout the day, they're generally in the same room or outside in the garden together, except when the little ones go away for nap time. So they do things like circle time, where they sit and sing songs and listen to stories, they do puppetry, they do drawing/painting/play doh/other messy play or crafts, they do just free play where they can dress up or play in the different stations or look at books in the book corner, build with legos or blocks. They're outside a lot of the day, play in a mud kitchen, do games, they cook/bake. They also do forest school sessions where they learn about plants and nature and bugs, etc.
Then there is more formal emphasis on learning specific skills, like number and letter recognition, writing their name, mark making and how to hold a pencil, but it's not like a formal session, like "now everyone sit down and we are going to learn letters." They just weave it into the rest of the day, like when they are drawing, someone will come and help teach them to write their name on their paper, or they'll play a number game together or something like that. Or when they're out, they'll practice counting with rocks or sticks, etc. Honestly, that's what they do in reception as well, so it's not much more formal once they get to school, at least in key stage 1.
They also do a lot of focus on personal care, using the toilet independently, washing hands, setting the table for lunch, tidying up, dressing and undressing independently, and social skills like sharing, turn taking, resolving conflicts, etc. That's the most important stuff for school really. Schools honestly don't expect them to come in knowing much about letters or numbers. They cover all that in reception anyway, so there's no rush (and your lo might just end up bored if they already know all of that). If they can recognise and write their name, that's great. Mostly, they just need to be able to do personal care and hygiene things on their own and that's enough. If you need to work, I would definitely go with a nursery. I think it's silly to pay more for a childminder to be doing pick ups and drop offs, which you can get fuller coverage and not so much back and forth with a nursery.
My daughter has been in nursery from 9 months and we love it. She's 4 and leaving for school in September. I never would have done preschool as the hours don't work for us and she wouldn't have had as much expose to other kids like she does now being in a setting with babies all the way up to school age children who come back for holiday club out of term. Also, personally, I think a nursery setting is better (at least around here). The preschools here are either at the school (she'll be at school her whole childhood, there's no reason to be in a school environment when they're little) or they were voluntary run by parents with few qualifications (the one preschool close to us we would have considered sending her to got shut down because it was just parent run and they were so disorganised and they ended up locking a little girl in the preschool and going home because forgot she was there! No one found her until like 3 hours later when her mum showed up to collect her and could see her screaming on the other side of a locked door in the dark!). Obviously, that's a very extreme situation, but it's why we wanted somewhere that was more professionally managed.