What is the difference between Azure AD Connect and Azure AD Application Proxy connectors? They both seem to provide the some sort of connection between your on-premises resources to Azure Cloud. I would like to know how they differ; when to use one over the other etc. etc.
Azure AD Connect is a synchronization service between your on-prem active directory and Azure Active Directory. It effectively allows you to use your internal AD accounts to authenticate to external applications using SSO. It differs from ADFS in that the accounts are actually synced out to AAD. Think of it as an identity pump.
AD App proxy is a set of infrastructure that proxies calls to on-prem applications for authenticated users. Those users may have authenticated using AAD or integrated Windows auth. The concept is to offer access to an on-prem application to the outside world via federation. You can see a decent picture of the flow here.