Although SPIM faithfully simulates the MIPS computer, it is a simulator and certain things are not identical to the actual computer. The most obvious differences are that instruction timing and the memory systems are not identical. SPIM does not simulate caches or memory latency, nor does it accurate reflect the delays for floating point operations or multiplies and divides.
Another surprise (which occurs on the real machine as well) is that a pseudoinstruction expands into several machine instructions. When single-stepping or examining memory, the instructions that you see are slightly different from the source program. The correspondence between the two sets of instructions is fairly simple since SPIM does not reorganize the instructions to fill delay slots.