The first feature allows for Find My Friends-style location sharing. From the app's menu you can select 'Share Location,' which presents options for how long your real-time location will be shared, and who it will be shared with.
The second sharing feature is the more interesting one in my mind. It allows you to share your Google Maps trip information. Daniel Resnick provides the details:
Next time you’re on your way or running late, you can share your real-time location and trip progress from navigation as well. During your next trip, tap the “More” button on the bottom on the navigation screen, and then tap “Share trip.” When you share your trip with people, they’ll see your expected arrival time and can follow your journey as you head toward your destination. Sharing automatically ends when you arrive.
Although the two sharing features perform mostly the same function, this kind of trip-specific sharing seems the cleaner, simpler solution for many scenarios. The example of running late and wanting to provide real-time updates to those you're meeting is a good one. In that situation, you won't want to fiddle with choosing a specific period of time for your location to be shared – you might overestimate and need to manually turn off sharing, or underestimate and have your location stop being shared before you reach your destination. Trip-specific sharing seems like just the right solution, and it's a feature I'm eager to try out.