I think the two ways of phrasing it are slightly different:
prevent a shortage before the delivery arrives during 95 percent of the order cycles
means that in the long run, there will be a stockout in 5% of the order cycles, whereas
meet demand 95% of the time
is a little ambiguous, but to me it suggests you want to meet 95% of the demands, i.e., stock out for 5% of the demands.
The first measure is the type-1 service level (or cycle service level), while the second is the type-2 service level (or fill rate).
The two are not the same. For example, if you have 1,000,000 demands per order cycle and you stock out on exactly 1 of them per order cycle, then your type-1 SL is 0% (because you have a stockout in every cycle) while your type-2 SL is nearly 100% (because you meet virtually every demand from stock).
The formula that @KevinG included is the safety stock required to meet the type-1 service level (which, it seems, is the service level that the original statement was referring to). But I disagree that the two statements in your original question are equivalent.