The 68000 only has 16-bit bus so it was not generally considered a full 32-bit CPU back in the day. The Atari ST's name alludes to this; it stands for Sixteen/Thirty-two (and perhaps also Sam Tramiel). The TT had an 030 so was Thirty-two/Thirty-two.
The 68000 only has a 16 bit DATA bus. The address bus is 23 bits. The general purpose registers are 32 bits.
Data bus: 16 bits
Address bus: 23 bits
Address Register Size: 32 bits
Data Register size: 32 bits
Instruction size: variable (multiple of 16 bits)
As far as programming goes, it looks and acts like 32 bits. You are right that it is generally considered a 16/32 bit hybrid CPU.
