[assembly] Difference between JE/JNE and JZ/JNZ

In x86 assembly code, are JE and JNE exactly the same as JZ and JNZ?

  je : Jump if equal:

  399  3fb:   64 48 33 0c 25 28 00    xor    %fs:0x28,%rcx
  400  402:   00 00
  401  404:   74 05                   je     40b <sims_get_counter+0x51>

From the Intel's manual - Instruction Set Reference, the JE and JZ have the same opcode (74 for rel8 / 0F 84 for rel 16/32) also JNE and JNZ (75 for rel8 / 0F 85 for rel 16/32) share opcodes.

JE and JZ they both check for the ZF (or zero flag), although the manual differs slightly in the descriptions of the first JE rel8 and JZ rel8 ZF usage, but basically they are the same.

Here is an extract from the manual's pages 464, 465 and 467.

 Op Code    | mnemonic  | Description
 -----------|-----------|-----------------------------------------------  
 74 cb      | JE rel8   | Jump short if equal (ZF=1).
 74 cb      | JZ rel8   | Jump short if zero (ZF ? 1).

 0F 84 cw   | JE rel16  | Jump near if equal (ZF=1). Not supported in 64-bit mode.
 0F 84 cw   | JZ rel16  | Jump near if 0 (ZF=1). Not supported in 64-bit mode.

 0F 84 cd   | JE rel32  | Jump near if equal (ZF=1).
 0F 84 cd   | JZ rel32  | Jump near if 0 (ZF=1).

 75 cb      | JNE rel8  | Jump short if not equal (ZF=0).
 75 cb      | JNZ rel8  | Jump short if not zero (ZF=0).

 0F 85 cd   | JNE rel32 | Jump near if not equal (ZF=0).
 0F 85 cd   | JNZ rel32 | Jump near if not zero (ZF=0).