Spoofing can be done many ways, but it's usually something like submitting a day order at an unreasonable price, then cancelling, say 10ms later.
Of course, reality is a bit more nuanced than that.
Source: I've worked in IT in Finance my entire career and have often dealt with SEC/FINRA/FBI requests for order history, and identifying which of our client(s) made the orders. Typically for specific tickers on specific dates, but sometimes for all tickers on specific dates, or for specific tickers for several years. Last I had to run these reports, it was for a small dark pool (like an exchange with unpublished prices). We typically had 10s of millions of orders a day. Quite a bit smaller than an HFT firm will be handling, but still quite a bit of data to work with and have to hand over on DVDs.
Spoofers put out orders without intention to trade. In fact, usually they would be horrified if their entire order trades. Their order price is not based on another market; their only intention is to impact prices in the book where they put the spoofing order. To achieve that, they often use disproportionately large order sizes, such as posting quantity 1000 where most other orders are between 1 and 20. Often they keep “applying the pressure” on the market by modifying the large spoofing order multiple times towards the market - moving the sell order lower and buy order higher - not as a response to changing market conditions in some other instrument but with the sole intention of impacting the price in the book in question.
Layering and spoofing are not done in good faith: there is never any intent to trade, just to convey a false appearance of market demand.
So to be clear, the HFT firm that places orders in the market want to trade those offers. They're comfortable placing those orders more competitively than your average punter because they can respond to market moving events quicker.
Layering and spoofing is something different - you're placing orders in order to make people think you want to trade, but you don't.
It's like asking me what's the difference between Al Gore offering you money to tackle climate change and a climate change denier offering you money to tackle climate change? Well one of them is clearly lying.
Perhaps they were unable to find otherwise legitimate trades from the traders ?