To give a clear-cut definition of spam this common misconception that "transactions bid for blockspace" has to be dispelled first:

Transactions bid for (more or less timely) confirmation, not space in blocks.

In fact "purchasing blockspace" is an undesired side effect to real Bitcoin users. If a new type of address was introduced whose transactions were half the size of the current ones a lot of users would adopt the new format just to pay half the fees at any given feerate. If you could confirm your transaction by purchasing no blockspace at all you would (and that's the idea behind LN: a single onchain tx supports a theoretically infinite number of offchain balance updates of that tx). This dynamic leads to a virtuous cycle where tx footprint gets smaller, users pay less fees, and so more users can use the chain.

On the other hand spammers are true purchasers of blockspace, something that Bitcoin is not designed for (and thanks to the SegWit discount they even get a 4x cost reduction byte per byte). This leads to a vicious cycle where only just a few spammers can quickly purchase all the available blockspace, spike the fees and so less people can use the chain.

Bottom line, since the legit group of bidders want to minimize their purchase of blockspace, while the spammers want to maximize it (and even gets a discount) there's only one possible outcome that we've already seen plenty of times: denial of service. Obviously all that is immaterial to the fees. If someone paid 10 bitcoins in fees to inscribe a hi-res video over the next 1500 blocks as one huge tx per block, that's still spam.