They don't all mean "to pay money" - in fact none of them mean just that.
"Buy" means "to pay money and obtain something" i.e. you pay money in exchange for the product or service. This is the verb form.
In noun form it means the item that was bought.
"Purchase" is a synonym for buy and means the same when used as a verb and noun.
"Buy up" means to buy everything available in the store.
She bought up all the shoes that were on sale.
"Buydown" is a financial term used to mean paying off some part of a loan and reducing interest rates.
A mortgage-financing technique with
which the buyer attempts to obtain a
lower interest rate for at least the
first few years of the mortgage, but
possibly its entire life.
As a crude rule of thumb, if you:
- spend something to do something
... then you spend it before you get or achieve the second thing. Here are some examples:
- We spent a lot of money to ensure the highest quality of workmanship.
- It's time to spend money to create jobs.
- There's no hiding from the fact we spent money to get players in.
In these instances, the infinitives are infinitives of purpose. In other words the infinitive tells us the goal of the spending activity.
In contrast if you:
- spend something doing something
... then you spend it as you are doing it. In other words the spending something and the doing something are happening at the same time:
- We spent a long time cleaning up after the party.
- We spent a lot of energy exercising and fretting over our physical condition.
Notice that in these instances, the -ing-clause tells us how we spent something, not necessarily why we wanted to spend it. Consider the following examples:
- We spent a lot of time getting nowhere
- We spent a lot of time being chased be photographers
Here we did not spend the time with the goal of not making progress or with the goal of being chased.
Gerund participle forms of verbs often indicate simultaneity, in other words they show that two actions are happening at the same time:
- He was run over crossing the road.
- Speaking with his mouth full, he asked me what I'd been doing.
The Original Poster's Question
*We spent a lot of time to shop.
We spent a lot of time shopping.
The Original Poster needs to use the second sentence here. The reason is that the spending time happened concurrently with the shopping. The two activities happened together.
Best Answer
Spending a lot of money "to buy" a house would be taken the same as spending a lot of money on/for a house, meaning that the price was high. (Of course, few people buy a house outright; they take out a mortgage and pay it off bit by bit, paying much more, over the years, than the price; however, one still speaks of the price as "how much you pay" for the house.)
But paying a lot "buying" a house can refer to paying a lot WHILE buying the house. This means the down payment, plus all closing costs, which are the additional up-front expenses incident to the purchase transaction. Closing costs can include many types of fees (legal, registration, title search, appraisal, termite inspection, earthquake report, to name a few), plus "points" if applied. In some times and places, these costs could run several thousand dollars—a big deal