>He was **caught up *to*** by her.†   

He had been ahead of her but she narrowed the distance between them and managed to come "alongside" him (literally or figuratively).

> She caught up to him.

Same as above, intransitive verb.

> He was caught up by her.

Transitive verb in passive voice: she brought him "up to speed" on the matter. She gave him the information he lacked.

†Compare:

> The chair was **sat down *on*** (by someone)
>
> Having got off to a good start he was briefly in the lead but was soon **caught up *to*** by the other runners.