Section 1624 is the exception § 1622 defers to. Subdivision (a) makes the listed contracts invalid unless they, or some note or memorandum of them, are in writing and subscribed by the party to be charged or that party's agent. The requirement is a signature from the person being held to the agreement — not a formal contract, not both signatures, and not necessarily a single document.
The list has seven entries. An agreement that by its terms is not to be performed within a year of the making. A special promise to answer for the debt, default or miscarriage of another, except as provided in § 2794. An agreement for a lease longer than one year, or for the sale of real property or an interest in it — and where such an agreement is made by an agent, the agent's authority must itself be in writing subscribed by the party charged. An agreement employing an agent or broker to buy, sell or lease real estate for longer than a year, or to find a buyer, seller, lessee or lessor, for compensation or commission. An agreement not to be performed during the promisor's lifetime. An agreement by a purchaser of real property to pay a debt secured by a mortgage or deed of trust on it, unless the assumption is specifically provided for in the conveyance. And a commitment to loan money or extend credit above $100,000 not primarily for personal, family or household purposes, made by someone in the lending business — with residential one-to-four-unit lending deemed to be for personal purposes.
Subdivision (b) then carves out qualified financial contracts on defined conditions. Two things about the first entry catch people out: the test is whether the agreement by its terms cannot be performed within a year, not how long it in fact took, so an open-ended arrangement is usually outside the section. And the section says the agreement is invalid, not that it never happened — doctrines such as part performance and estoppel operate around it, which is exactly the argument to take to a lawyer.