Office Expenses are costs related to the operation of your business. These include items such as web site services, computer software, domain names, merchant fees, desktop computers, etc. However, higher priced office expenses, e.g. computers, smartphones, are considered assets and can be depreciated.
Supplies are items that aid in the operation of your business. These include items such as printer ink, paper clips, paper, pens, staples, record keeping supplies, janitorial supplies, break room supplies, etc.