A computer can perform operations, each of which is is assigned a numeric code called an opcode. Since humans are terrible at memorizing lots of similar numeric codes, mnemonics are used as textual abbreviations. It's much easier to remember ADD than 05, for example.
Opcodes operate on registers, values in memory, values stored on the stack, i/o ports, the bus, etc. They are used to perform arithmetic operations and move and change values. Operands are the things that Opcodes operate on.
Byte codes are another term for op codes, especially when they are used to describe higher level constructs as is the case with the Java Language's JVM (Java Virtual Machine). For instance, byte code 1A might be the "iconst_2" instruction which pushes the number 2 on the stack. This is a slightly higher level of abstraction, than opcodes, which might need to load the number 2 into a register, and then push the register's value on the stack.