To answer your question, payment methods are certainly stored in the database, they don't have their own table but are stored in the core_config_data table
To get the payment methods you can do the following:
select * from core_config_data where path like 'payment/%active' order
by path;
SELECT * FROM core_config_data WHERE path LIKE 'payment/%active' ORDER BY path;
This will display values with their ACTIVE bit (yes/no):
payment/paypal_express/active 1
payment/wps_express/active 0
The means that PayPal Express has "Enabled = YES" on Admin Whilst WPS Express has "Enabled = NO" in the Admin.
I hope this helps with your query.