There are subtle differences in meaning.

“I earn $500 *[each](https://www.google.com/search?q=each&tbs=dfn:1 "“each” at Google Dictionary")* month” says that each month, considered separately, the sum of your receipts is $500. This can mean that the sum equals $500 *exactly*. But it can also mean $500 *at least*. For example, you can write:
> I earn $500 each month. During peak months, I earn as much as $800.

"I earn $500 *[per](https://www.google.com/search?q=per&tbs=dfn:1 "“per” at Google Dictionary")* month” express a *rate*, or linear relationship, between time and money. It means that over *n* months, the sum of your receipts is *n* × $500. Again, this can mean that the monthly sum equals $500 *exactly*. But it can also mean $500 *on average*. For example, you can write:
> I earn $500 per month. This is considering the year as a whole. The summer months are slower, but I always make it up over the holidays.