Most of the 24 character strengths map onto one or two of the Big Five: zest and humour onto extraversion, curiosity and creativity onto openness, perseverance and prudence onto conscientiousness, kindness and fairness onto agreeableness. The trait the strengths mostly leave out is neuroticism, because the classification describes what is good about people and not what troubles them.
The evidence
Peterson and Seligman (2004) built the classification from moral traditions rather than from the statistics of personality, so there was no reason to expect it to line up with the Big Five, and the test of whether it does came afterwards. Macdonald, Bore and Munro (2008) gave people both a strengths inventory and a Big Five measure and factor-analysed the 24 strengths. The strengths fell into four broad groups rather than six virtues, and the four lined up with extraversion, openness, conscientiousness and agreeableness. Emotional stability was the one Big Five trait the strengths did not cover well: there is no strength called calmness, and the nearest, hope and self-regulation, are only partly about it.
McGrath (2015) pooled very large samples from several countries and found a coarser structure still: three broad groups, which he called caring, inquisitiveness and self-control. Caring gathers the strengths that look like agreeableness (kindness, love, gratitude, teamwork), inquisitiveness those that look like openness and extraversion (curiosity, creativity, zest, love of learning), and self-control those that look like conscientiousness (prudence, perseverance, self-regulation, judgment). The Big Five and the strengths are two maps of much the same territory, one drawn from how people describe behaviour and the other from what cultures have called virtue.
What the overlap does not mean
It does not mean the strengths test is a Big Five test with different labels. The strengths are narrower than the five domains, closer in grain to the thirty facets of the Big Five test, and a strength such as spirituality, appreciation of beauty or forgiveness has no close Big Five equivalent at all. It does not mean a high neuroticism score forbids high strengths; the two measures hardly touch, so a person who worries a great deal can still score high on kindness and curiosity. A score on either measure is not a diagnosis of anything.
What it means for your results
If you have taken both tests, expect the broad shape to agree: a high openness score usually sits beside high curiosity, creativity and love of learning, and a high conscientiousness score beside perseverance, prudence and self-regulation. Where a strength is high and the matching Big Five trait is not, the strength is telling you something the broader trait averaged away. The strengths profile is the finer map; the Big Five is the one with a comparison sample, so only the Big Five result carries a percentile.
The character strengths test has 96 items, takes ten minutes and is scored on your device, with all 24 strengths drawn on strips against the possible range of 4 to 20.