There are so many types of memory that is hard to answer.
What was "standardized" (wich standard ?) was the byte (octet) as a fundamental size on a computer. This means that, usually, computers have how to deal with 8 bit numbers, even if they are 32 bits. A byte is 8 bits anywhere, but the computer WORD might have other sizes, multiplies of a byte (ex.: 32bit word wich is composed of four bytes etc). It might even arrange those bytes in different orders (MSB first, LSB first etc).
But, on memories, you might find a lot of types. You might find a 8 bit EPROM, or a single bit RAM (where you need to group 8 ram chips to get a single byte, etc). Or even full 64bit memories that transfer 64bit words at a time.
But, even when all the memories have different word sizes, you can still ADDRESS all memories in 8bit boundaries.
For example :
If your "cell" was 32 bits, thats how the program would be stored in memory:
100 add r1, r2, r3
101 sub r3, r5, r1
102 br 100
If your "cell" is 8 bits, thats how it is stored in memory :
100 add r1, r2, r3
104 sub r3, r5, r1
108 br 100
In the past, some computers worked like the first example, having memories cells of 32bits (or 36, or 24 etc.), so, in that case, the "standardization" was to accept a single memory "cell" size (8bits) and work other sizes from that.
This does not mean that a computer cant access the RAM in lumps of other multiples of 8 bits (16, 32, 64, etc.). You might have instructions like
MOV EAX, [BP+10000] // hipotetical, i dont know if this addressing mode exists
// wich will transfer 4 bytes in a single cycle into the EAX.
But the BP+10000 in the instruction still sees the memory as made out of 8bit cells.