They aren’t talking to each other, they get used separately for their own purposes. I use WooCommerce for online shops, and Events Manager for the calendar of events. I’ve built quite a few sites for wineries, and some of them require both a shop and a calendar.
Most of the sites I’ve built with both plugins don’t have ticket sales, but where they do, a couple use Events Manager Pro for ticket sales (where they need to be tied to reserved seats) and a couple use WooCommerce (where it’s just entry tickets, no reservation required, and no real integration with Events Manager). One or two even use Gravity Forms for ticket sales (great for custom forms with lots of fields, e.g. conference registration).
The two plugins sit happily together, no conflicts. Both are easily customisable through settings, template overrides, and action/filter hooks.
cheers,
Ross