ARM Processor Register Vs Word

What's the difference between a register and a word? As far as I know,

• 8 bits = 1 Byte, 32 Bits = 4 Bytes = 1 Word
• A register is 32 bit, which means size of 1 register = 1 Word
• Then probably, the processor having a total of 16 registers should have a total of 16 X 1 = 16 words.
• Then what does 2^30 memory words mean in an ARM Processor? ARM Operands
• Also, is this 2^30 words concept somehow related with the 32-Bit or 64-Bit computer we use?

Can someone help me get this concept right? Thanks in advance!

Being a 32bit architecture, the addressing area is 2^32 = 4GB.
And since each word is 4 bytes long, the total area in word is 4GB/4 = 1G words (2^30)