I believe a soft fork is backwards compatible, meaning you don’t necessarily have to update Bitcoin core. A hard fork means upgrading core is a must to stay in sync with the blockchain but feel free to correct me if I’m wrong. 

 Soft fork is backwards compatible, there is no break in the network rules, only an additional restriction within the rules.

Example: the current rule for blocks is 1MB limit, so 2MB limit would be a hard fork because it breaks the rules. However we *could* do a soft fork down to a 700KB block if we wanted, because it doesn’t violate the 1MB limit on older nodes. But this also allows us to add features, timelocks, new signature types, new rules about spending coins, etc.

In short a soft fork is a backwards compatible upgrade. All old nodes and software will still work fine as if nothing happened.

A hard fork is a breaking change. It creates an entirely new set of rules and if you don’t upgrade, either your bitcoin is gone, or more likely, the new upgrade just creates another shitcoin and splits into a separate network.