What's the difference between R_386_GOT32 and R_386_GOT32X?

Both relocations have the same effect and the calculations are the same, but R_386_GOT32X relocations allow the linker to optimize the instructions used for the calculation, using immediate operands instead of memory operands under certain conditions.

H. J. Lu (Intel engineer who introduced R_386_GOT32X) explains it in the IA32 System V ABI mailing list:

X86 instruction encoding supports converting some instructions on memory operand with GOT32 relocation against symbol, foo, into a different form on immediate operand if foo is defined locally. Those instructions are:

call *foo@GOT[(%reg)]       => nop call foo or call foo nop
jmp *foo@GOT[(%reg)]        => jmp foo nop 
mov foo@GOT[(%reg1)], %reg2 => lea foo[@GOTOFF(%reg1)], %reg2

When osition-independent code is disable,

test %reg1, foo@GOT[(%reg2)] => test $foo, %reg1 binop
foo@GOT[(%reg1)], %reg2      => binop $foo, %reg2

where binop is one of adc, add, and, cmp, or, sbb, sub, xor instructions.

I am proposing to add a new relocation, R_386_GOT32X, to i386 psABI. Instead of generating R_386_GOT32 relocation agasint foo for foo@GOT(%reg), we generate R_386_GOT32X. R_386_GOT32X relocation can also be used without the base register for the global offset table, foo@GOT, when position-independent code is disable. In this case, the static base address of the global offset table will be used instead. Linker can treat R_386_GOT32X the same as R_386_GOT32 or it can perform the transformations listed above.

Indeed, according to the IA32 System V ABI document you linked (section A.2):

Optimize R_386_GOT32X Relocation

The Intel386 instruction encoding supports converting certain instructions on memory operand with R_386_GOT32X relocation against symbol, foo, into a different form on immediate operand if foo is defined locally:

Convert call, jmp and mov Convert memory operand of call, jmp and mov into immediate operand.

Memory Operand	Immediate Operand
call *foo@GOT(%reg)	nop call foo
call *foo@GOT(%reg)	call foo nop
jmp *foo@GOT(%reg)	jmp foo nop
mov foo@GOT(%reg1), %reg2	lea foo@GOTOFF(%reg1), %reg2

Convert Test and Binop Convert memory operand of call, jmp, mov, test and binop into immediate operand, where binop is one of adc, add, and, cmp, or, sbb, sub, xor instructions, when position-independent code is disabled.

Memory Operand	Immediate Operand
call *foo@GOT	nop call foo
call *foo@GOT	call foo nop
jmp *foo@GOT	jmp foo nop
mov foo@GOT, %reg	mov $foo, %reg
test %reg, foo@GOT	test $foo, %reg
binop foo@GOT, %reg	binop $foo, %reg
call *foo@GOT(%reg)	nop call foo
call *foo@GOT(%reg)	call foo nop
jmp *foo@GOT(%reg)	jmp foo nop
mov foo@GOT(%reg1), %reg2	mov $foo, %reg2
test %reg1, name@GOT(%reg2)	test $foo, %reg1
binop name@GOT(%reg1), %reg2	binop $foo, %reg2