yes, it’s the same AMR, whichever vendor.
In other words, TMZ, instead of a call drop, the call is kept with AMR under poor radio conditions, so there is more erlang in the cell. That makes perfect sense.
The smooth transition you’re talking about is the fact that an AMR phone can start a call in FR and change to HR if asked by the network. Whereas a “dual rate” phone must keep the same codec from start to end of call (within the same cell).