Does Chill Touch Prevent Druid’s Wild Shape from Recovering Hit Points?

Does the Chill Touch cantrip’s secondary effect prevent a Druid from regaining hit points via Wild Shape?

Chill Touch reads:

… On a hit, the target takes 1d8 necrotic damage, and it can’t regain hit points until the start of your next turn.

Wild Shape:

… When you transform, you assume the beast’s hit points and Hit Dice.

RAW: Is "assume" the same as "regain"?