"probably" but not always. I have worked on a few projects that saved 70-90% of costs for AWS -- but these all were starting from a position of auto scaling out a ton of ec2 (on demand full cost instances) to batch process huge amounts of data. In both scenarios by optimizing the batching to align tasks to pack as much as possible into (just short of hour long) hour long windows and converting to a (wide list of ec2 types to avoid contention lockout) spot instances there was easy fodder for the improvement.

But yeah -- no one should see their bill change by that much without understanding exactly what was done to trigger it. Even in the best cases, there are always tradeoffs that must be known and accepted.