The basic principles of contract
Quick reminder: in the law of contract “losses” and “damages are” different, though related things.

Losses are pecuniary misfortunes that you might suffer as a result of a breach of contract. They can be divided into:

Direct” losses, that are the natural and foreseeable consequence of breach of contract.
Indirect” or “consequential” losses, which are a more speculative nature.

Note that “loss of profit” and “loss of opportunity” are not judicially recognised categories of loss: they can be either direct — for example, foregone interest on a defaulted payment — or indirect — the winnings you would have got from putting that defaulted payment on a rank outsider who came good in the 2:35 at Kempton — but if in doubt (i.e., not a natural consequence of the breach) assume they will be indirect

Damages are the amounts a court orders a naughty counterparty to pay to an innocent to compensate for its loss of bargain (in a contract) or atone for its wrongdoing (in a tort or breach of trust). They may, or may not, be the same amount as the actual losses suffered:

General” damages compensate for direct losses.
Special” damages relate to indirect losses. They are rare in contracts, even when not specifically excluded which, in finance contracts, they usually will be.
Punitive” or “exemplary damages do not compenstate for loss at all, but rather punish a wrongdoer for outrageous behaviour. These are not available under English contract law but may be awarded — extremely rarely — in tort or for breach of trust.
There is also an “Account for profit”: an order to hand over profits made through the misuse of someone else’s physical or intellectual property. This remedy is not available for a simple breach of contract.
Grievances and remedies, charted
Grievance Remedy Contract Tort Fiduciary
Direct loss General damages Yes Yes Yes
Indirect/consequential loss Special damages Usually No Usually No Usually No
Egregious wrongdoing Exemplary/punitive damages No Yes Possibly
Profiting at owner’s expense Account for profit No Yes Yes
Formation: capacity and authority · representation · misrepresentation · offer · acceptance · consideration · intention to create legal relations · agreement to agree · privity of contract oral vs written contract · principal · agent

Interpretation and change: governing law · mistake · implied term · amendment · assignment · novation
Performance: force majeure · promise · waiver · warranty · covenant · sovereign immunity · illegality · severability · good faith · commercially reasonable manner · commercial imperative · indemnity · guarantee
Breach: breach · repudiation · causation · remoteness of damage · direct loss · consequential loss · foreseeability · damages · contractual negligence · process agent
Remedies: damages · adequacy of damages ·equitable remedies · injunction · specific performance · limited recourse · rescission · estoppel · concurrent liability
Not contracts: Restitutionquasi-contractquasi-agency

Index: Click to expand:
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What an agent must do if it profits (without permission) with its principal’s property; what a thief (or breacher of copyright) must do to its victim with the ill-gotten gains of its misfeasance. Importantly, not what a breacher of contract must do to an innocent counterparty: there the measure of compensation is the innocent party’s loss.

Account for profits is a common law remedy for misuse of another’s property. It is not a remedy for breach of contract.

Not the same as loss of profits

The remedy of special damages for loss of profits — when available, which will be hardly ever — compensates an innocent party to a contract for opportunities and profits she would have been able to take had the guilty party not breached the contract. This is different from the remedy of “accounting for profits”, which is a common law remedy for misuse of someone else’s property where the guilty party must disgorge to the owner any profits it has actually made in breach of his contractual or fiduciary duty.

See also