Contact List needs to segregate customers & Vendors!
The Contacts app is a representation of the Contacts table which contains customers, vendors and employees. If you want to show only vendors or only customers you can do this one of two ways.
You can add new Grid Views to show only Vendors or only Customers. This is the easier option and should achieve what you want.
Step 1 - Go to Manage Apps and click Edit App for the Contacts app.
Step 2 - On the Contact List screen click on Copy
Step 3 - Rename the screen and click OK
Step 4 - On the newly created screen click Customize
Step 5 - Click on the Contacts grid, in the right hand column expand Filters & Views, and click the Grid Views button
Step 6 - Click 'Add another view', enter a Filter name, if you want this new view to be the default view when the Contacts List is loaded check the 'Set as default' box, and then click 'Add Criteria'. The field you will be looking for is EntityType and the value will be 'Vendor' or 'Customer' depending on which view you are adding. You can also make this your vendor or a shared vendor if you wish by clicking 'Add 'ADD' condition'. Have a look at the other views to see how they are set up to get an idea of what you want.
Option 2 - You could build your own apps for Customers and Vendors though this is probably unnecessary. There is a chance that further down the line when functionality is added to Beta a Vendor app might be added.
I hope this helps. Let me know if you have any further questions or would like anything to be clarified.