How to categorize money transfer by check between two business accounts

There is no such thing as equity distributions, there is an equity draw though

transferring funds from one bank to another is just moving money, there is no category for that, it is a bank transfer (assuming the two accounts are for the same business)

Thanks so much for the clear answer.

The reason why I brought up "Shareholder's Equity: Distribution" is that my bookkeeper categorized the same kind of transaction as that last year. I will categorize it as "transfer" from now on.

She categorized all the money transfers from my business account to my personal account as "Shareholder's Equity: Distribution" last year. Is that correct? Our CPA approved that too. Should I use "Equity draw" instead?

What if the transfer in from a sister company? How would you categorize that on both sides? 

If you are going from a business account to your personal account, then your bookkeeper / CPA is correct as you are removing money from the business.

However, your question stated you were making a transfer between two business accounts (assumingly owned by the same business), thus you are not removing money from the business, so it's just a bank transfer.