We have both since we are remote.
There is so much good info in this thread - I need to do some septic maintenance!
For the well, there will be a tag on the well head that will direct you to the folks who installed it, you can work from there. The county also should have a record of the permit.
Our well is set up so that the pump can be replaced easily - not cheap, easily
See if your can be as well.
Make sure the well head is free and clear of any debris or growth.
If the above was redundant, sorry!