There aren't that many differences between AP and TCC, I think it's more of a mindset tbh. Both include babywearing, breastfeeding, co-sleeping and generally being close to the baby.
However AP tends to be a bit more baby-centred, and TCC tends to be a bit more parent-centred, if I've read them both right.
In TCC you do carry the baby around with you but it's while you get on with the rest of your life, so that the baby is almost a satellite to the mother. You'd get on with your housework with the baby in a sling but not be too fussed about having to interact constantly with the baby.
Jean Leidoff does come up with some ways to make TCC work in modern life at the end of the book. She suggests you get together with a like-minded friend and clean and tidy each other's houses, for example. Of course in modern life we're never going to be quite as active as the Yequana but we can do housework, cook, walk the dogs, go shopping (and walk rather than take the car) all with the baby watching quietly from the comfort of a sing or baby carrier.
I think as with all of these things the "mantra" is "take what you need, and leave the rest."