Soft Fork
A rule change that only tightens the rules, so nodes that have not upgraded still accept the new blocks.
Since the new rules are a subset of the old ones, everything valid under the new rules was already valid under the old, and out-of-date nodes keep following the chain without noticing the change. This lowers the coordination burden, but it depends on a large majority of block producers enforcing the tighter rules, otherwise blocks that break them would be accepted by the un-upgraded majority. Bitcoin has used soft forks for major changes including pay-to-script-hash, SegWit in 2017, and Taproot in 2021. The hidden cost is that an un-upgraded node believes it is validating fully while it is in fact not checking the new conditions at all.
In practice
SegWit was deployed as a soft fork, so nodes running older software continued to accept blocks containing SegWit transactions without understanding the new structure.
The common misunderstanding
A soft fork is not necessarily a smaller change than a hard fork; compatibility describes how the rules relate, not how significant the upgrade is.