Baby carrots are not, in fact, small carrots. They are misshapen carrots that would not sell unless they were carved into "baby carrots".
The ones I've gotten that still have the tops on them, and the outer skin, absolutely are; IME, what you are referring to are generally sold as “baby-cut” or “petit” carrots, rather than “baby" carrots.
In the UK the closest I've seen or heard of are both 'real' (whole) carrots:
Chantenay - https://www.waitrose.com/ecom/products/waitrose-chantenay-ca...
'Baby topped' - https://www.waitrose.com/ecom/products/waitrose-1-baby-toppe...
What?! Citation sorely needed. I do, and in my experience 'big' (I would've said 'normal') carrots are stocked more abundantly than any other.