買い物 and 購入: shopping as an activity and the item purchased
Distinguish 買い物をする and 買い物に出かける from an item followed by を購入する. Going shopping does not identify the goods actually bought.
Shopping as an activity
買い物, read かいもの, means shopping. 仕事の帰りに夕食の買い物をした。 says that someone shopped for dinner on the way home from work.
買い物をした describes the shopping activity here. Read its function in this sentence instead of automatically treating 買い物 as the name of merchandise to purchase.
Attach the item to 購入する
購入, read こうにゅう, means purchase. 新しい自転車を購入する前に何台か試した。 says that several bicycles were tried before purchasing a new one.
自転車を supplies the purchase object, while 試した reports the completed trial. In this construction, do not substitute the shopping activity for the bicycle as the item being bought.
The purpose of going out and the purchase result
必要な物をメモしてから買い物に出かけた。 says that someone noted the needed items and then went shopping. 買い物に gives the purpose of going out.
Going shopping and reporting which goods were purchased are different pieces of information. This construction does not establish a rule excluding merchandise-related meanings of 買い物 in every context.
Does 買い物に出かけた。 identify the goods that were purchased?
Show the answer and why
No. It gives the purpose and action of going shopping. The actual items purchased need separate information.