Some product can be target for multiple discount campaigns, but only one discount can be applied to a product/variant. Discounts from different campaigns do not stack.

If at the time of campaign (B) activation a product/variant already had an active discount from another campaign (A), then this product/variant is skipped and the discount of the current campaign (B) is NOT applied to it.

Deactivating the previous campaign (A) will NOT apply the discount of the new campaign (B) - for this you need to Refresh the new campaign (B).