An HSA account can be operated and accessed like a checking account.
The HSA account I have been using has a debit card. I can use it only a specific types of vendors. This makes it easy to pay co-pays and to pay for prescriptions.
The website can also be used to pay providers. I find this works best If the amount of the bill isn't known until after the insurance company processes the bill.
I can also use the website to pay me back, if I don't use the debit card to pay a medical bill. This involves more paperwork becasue the HSA custodian wants me to submit the Explanation of Benefits (EOB) from the insurance company.
The HSA custodian I use doesn't have a checkbook option. I have found the other two options (debit card and website) meet my needs.
The system connected to the debit card is supposed to not allow you to use the card at non-medcial vendors. It also can be used at pharmacies. The record keeping of the system, along with these restrictions allows me to know that I have only used it for allowable expenses. I don't think the checkbook provides that benefit.