What is the difference between general and community hospitals?

No difference. Large general hospitals may have more specialties and capabilities to do more specialized tests/procedures. Financially, they are no different - they can be for profit or non-profit. Non-profit is a misnomer created by the U.S. Tax code. All organizations need to make a profit to operate (eco 101). The difference is who gets the returns - shareholders or re-investing in the organization.