This image from Simpson Strong-Tie (the manufacturer of most connectors you'll see) illustrates the connectors commonly used to connect framing members along the load path from roof to soil.
The exceptions are Roof/Wall connectors, which are designed to resist wind uplift, and hold downs, which are designed to resist both wind and seismic loads.
Connectors must be fastened with the fasteners specified by Simkpson. Find that information here.