Yes, no, sort of.
I mean shampoo is definitely not the same as laundry soap.
And even between shampoos, there are differences (as anyone with skin conditions can attest).
Are products in any one category largely the same? Yes. But there are differences.
Most lotions contain dimethicone, a silicone relative.
They both work by being moisture barriers, preventing moisture loss (for hand lotion).
As someone who struggles with skin issues, I don't even bother with lotions that don't have dimethicone, they're practically useless for me.