How, I wondered, did this term come to have its present meaning, related as it is to capture (both coming from the Latin capere, to take. OED provided the answer.
The earliest senses are:
1. a. Taking, catching, seizure, capture. now rare.
1382 WYCLIF 2 Peter ii. 12 Beestes, kyndeli in to capcioun [Vulg. in captionem], or takinge
b. Law. Arrest or apprehension by judicial process. (esp. in Scotch law.)
1609 SKENE Reg. Maj. Table, 70 The forme of the breive of caption of ane debtour.
2. The action of cavilling or taking exception; an objection or cavil; fallacious or captious argument; a quibble, sophism. (L. captio.)
1605 BACON Adv. Learning II. xiv. §6. 55 The degenerate and corrupt vse is for Caption and contradiction.
3. Law. ‘That part of a legal instrument, as a commission, indictment, etc., which shows where, when, and by what authority it is taken, found, or executed’ (Tomlins Law Dict. 1809). This appears to be short for ‘certificate or note of caption or taking’; and it is sometimes used for the ‘making or execution’ of this certificate.
1670 BLOUNT Law Dict. s.v. Caption (Captio), When a Commission is executed, and the Commissioners names subscribed to a Certificate, declaring when and where the Commission was executed, that is called the Caption.
The foregoing is sometimes explained as ‘the beginning or heading of a warrant, commission, or indictment’, whence comes
4. The heading of a chapter, section, or newspaper article (chiefly used in U.S.). Also used (orig. U.S.) for the title below an illustration; in cinematography and television, a sub-title. Also attrib. and Comb.
1789 J. MADISON Writ. (1904) V. 355 You will see in the caption of the address that we have pruned the ordinary stile of the degrading appendages of Excellency, Esqrs. &c. 1821 Massachusetts Spy 24 Oct. (Th.), [The statute] is under the caption of ‘Fees in the Secretary’s office’. 1848 BARTLETT Dict. Amer., Caption: This legal term is used in the newspapers where an Englishman would say title, head, or heading. 1854 N. & Q. Ser. I. IX. 245/1 [A review] having three works as the caption of the article.
Interesting that Bartlett in the 1848 cite notes the sense as purely American. It clearly crossed the Atlantic soon after, as evidenced in the 1854 cite from the British periodical Notes & Queries.