Apparently, this term doesn't mean much. Why? Well, if a semilattice is complete (all subsets hold the meet / join property), then it will be complete in the other direction, making it a complete-lattice

[A] complete meet-semilattice has all non-empty meets (which is equivalent to being bounded complete) and all directed joins. If such a structure has also a greatest element (the meet of the empty set), it is also a complete lattice.

Why does this term exist? Probably, because we only care about completeness for one operation, either just the meet or just the join.

References

https://en.wikipedia.org/wiki/Semilattice#Complete_semilattices