I think that you are correct about it being a box turtle.
He/she could use a beak and nail trimming.
Someone more experienced with box turtles should be along soon.
Is the other tortoise a decoration?
Your box turtle could do with actual substrate and a larger waterer. The shell looks very dry and box turtles like a lot of moisture. You want to make the habitat suited for the needs of your species so that means you'll need to make quite a few changes as it seems you've just learned what species you keep. Read in the American box turtle section for ideas (especially the pinned care sheets).
The curly nails are sometimes an indication of MBD. What are you doing for UVB light? What are you feeding? Box turtles are omnivores and need a lot of variety.
They don't get used to not having it. Do you take your turtle outside for regular access to real sunshine? If so, then a uv lamp is probably not needed.
Since box turtles eat animal protein, they have access to some dietary d3, but synthesizing their own from UVB light is likely still important (there is some debate though). Mealworms are a popular feeder, but lacking in a lot of the essentials and hard to dust or gut load with nutrients and vitamins. Diverse animal protein - pinkies, soldier fly larva, earthworms (earthworms are easy to dust with vitamins or gut load), etc. should be used.
Your diet is poor in calcium based on the foods you have listed, so even if there was enough dietary d3, your turtle won't have the accessible calcium it needs to use it. Changing up your diet is important. If you can't get the right foods in, tiny pinches of vitamin supplements are needed.
Beak and nail issues in box turtles point to deficiencies you need to address.
I would say a 3 toed but it's still very hard to tell with that shell damage. She needs a lot of changes to help her. Check out the box turtle section in the forum.
Been poor her whole life
She looks so unhealthy
Had her for twenty-two years
She outlived the person who gave her to uss
But she's active and doesn't seem depressed
My great Turtle
when she gets healthy cant wait