What's the difference between di.xml in the different etc folders?

Each module can have a global and area-specific di.xml file. Magento reads all the di.xml configuration files declared in the system and merges them all together by appending all nodes.

As a general rule, the area specific di.xml files should configure dependencies for the presentation layer, and your module’s global di.xml file should configure the remaining dependencies.

Magento loads The configuration in the following stages:

1. Initial (app/etc/di.xml)
2. Global (<moduleDir>/etc/di.xml)
3. Area-specific (<moduleDir>/etc/<area>/di.xml)

During bootstrapping, each application entry point loads the appropriate di.xml files for the requested area.

SOURCE

'di.xml' is used for set dependency.

You can place it in etc folder or frontend or adminhtml folder

but purpose to set it in different folder is :

1. frontend : all dependency which apply for frontend is needed to set in it, so developer can have clear idea about dependency applied for frontend development.
2. adminhtml : all dependency applied to admin should be placed at adminthml, so developer can identify it easily.
3. etc : Its for general dependency, so we can define dependency which can be used in both frontend as well as backend.

Different folder created for different dependency can make it easy to find any dependency applied on Backend or frontend or both.