Events are special time periods of the year which allow commanders to obtain loot including robots, weapons and their respective Titan counterparts, usually from two special crates which can be opened for 100 and 1000 of the event currency (a.k.a. tokens) respectively. However, the latest Icarus Cyber Show of 2020 featured a crate that costs 300 event currency, which replaced the crate that costs 1000 event currency (however, it contained items from the crate that costs 1000 tokens). Sometimes, they are limited, meaning they will happen once and only once, but sometimes are recurring, which means they will happen again (roughly) on the same date next year.
Operations are an exclusive feature of the game. When they begin, they allow the participating commanders to claim a free reward (item/currency) at the start. As the commander plays more matches, they will begin earning Operation XP (OXP), however they can obtain it in different ways too (watching ads etc). When the commander reaches a fixed amount of OXP, they will proceed to unlock the next 'card', and thus unlocking another reward.
By purchasing an Operation Pass with real money, a commander can obtain considerably better loot. Using Operation: Dark Nebula as an example, the first reward is 1M Ag, however by purchasing an Operation Pass a commander can obtain a Stellar Halo. Usually, each 'rewards lane' has a considerable difference in rewards from the other.