Yes Erik, you're right. It sure is true for an 8088 it is a 16 bit cpu with an 8-bit data bus. Registers by default are 16 bit, however you can still access the low or high byte like AL or AH of AX.

But this is hard to say for 251 since it has no default register size. It operates with 8-bit registers like standard 51 by default, while the registers can be grouped to word registers WR0 (R0 & R1), WR2 (R2 & R3) that are word sized, but also dword sized like DR0 (R0,R1,R2,R3), DR4 (R4,R5,R6,R7) etc.
Of course there are some that can be only word or dword accessed (WR16..WR30, DR16..DR28)
So in this notation one can also say it is a 32-bit controller. But this is far away from say ARM cpu, that really is 32-bit with default register size of 32bits, data bus of 32bits (it can also run in 16-bit bus mode but...)

So I prefer saying that it is an accelerated 8-bit cpu with 16-bit and 32-bit extended instructions.

Franc