Hello Chris
In PHP, it is more appropriate to refer to the outer and inner label, although the top and bottom labels are also used as terminology. The top label is the outer and the bottom is the inner. So in PHP, it is the outer label that is removed by the Label Switch Router (LSR) before the packet is passed to the adjacent Label Edge Router (LER).
In the case of MPLS VPN, a packet consists of two labels, the inner one is the VPN label and the outer one is the common MPLS label. So when PHP will be performed by an LSR it will remove only the outer label. The LER will then pop the VPN label before sending it to the CPE.
I hope this has been helpful!
Laz