Deal structure nomenclature

Had a somewhat obscure question about names for specific structures in deals. Let's say you have BuyerCo and SellerCo. SellerCo has a subsidiary, OpCo. BuyerCo purchases OpCo for equity, and now SellerCo has some % minority equity interest in BuyerCo - this new entity is CombinedCo. Is there a name for this structure / deal type?

Next, a financial sponsor recapitalizes CombinedCo with a mix of debt and new equity, but specifically buys out most of BuyerCo's interest. SellerCo rolls their equity over, and now BuyerCo has a minority interest in the equity ownership. Is there a name for this structure / deal type?

Trying to figure out how I can succinctly put this on my resume, anything would help. Right now I'm just saying "recapitalization of a company following purchase of another company's subsidiary"

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