Sunrise and Landrush are two separate events/periods of time relating to the delegation and launch of a domain extension (TLD). Both take place before the public launch of a TLD (when anyone can register a domain with the new TLD). There are financial or legal considerations for both.
Before a new TLD is released to the general public, some registries offer a "sunrise period", which allows brand and trademark owners to register their domains first.
The goal here is to prevent someone from registering a domain like iwantmyname.TLD before we get the chance. This helps prevent trademark violations and other legal issues after the launch.
For more information about sunrise periods, here's a helpful link:
After a sunrise period, the landrush period gives people the chance to buy domains before the general public, but often for a premium cost.
The people or companies who participate in the landrush period don't necessarily have any specific rights to domains with the new TLD (like trademark). They're just willing to pay extra for a better chance of securing their desired domain name(s).
Note that at iwantmyname we do not participate in sunrise or landrush periods and while for new TLDs that we carry we do offer pre-orders before launch, pre-orders are only processed during the public launch of the TLD, so customers don't have any priority access to new TLD domains or guarantee of securing the registration.