The language לקיחה (taking) a woman is used whether it is talking about betrothal or marriage. But when it says לקח לאשה with the prefix ל, it is only talking about betrothal that is the beginning of the לקיחה, not about entering the wedding canopy after betrothal. And moreover, this language is correct with respect to a levirate marriage, since that is also the beginning of לקיחה.

And moreover, it uses the language קנה (acquire) and קנין (acquisition) with respect to marriage to a woman. And this is the difference between the verb קנה and the verb כרה (buy): The verb כרה comes only on that which is acquired through selling, while the verb קנה includes all types of acquisition of something that will be his.