This is a post about the shade of meaning between "laconic" and "taciturn."

There really was a place called Laconia. It's where Sparta was. The OED says "laconic" means, first,  "Characteristic of the Laconians; Spartan-like" and quotes John Adams:

1787   J. Adams Def. Constit. Govt. U.S. Pref., in Wks. (1851) IV. 287   The latest revolution that we read of, was conducted..in the Grecian style, with laconic energy.

But that's not the meaning we want. We want definition #2, from the (unlinkable) OED: "Following the Laconian manner, esp. in speech and writing; brief, concise, sententious. Of persons: Affecting a brief style of speech." Example:

1888   A. K. Green Behind Closed Doors iii. 28   ‘Trust me’ was his laconic rejoinder.

Now, "taciturn" — an adjective based on "tacit" (silent) — has only one meaning: "Characterized by silence or disinclination to conversation; reserved in speech; saying little; uncommunicative." Examples:

1771   T. Smollett Humphry Clinker II. 107   Grieve..was very submissive, respectful, and remarkably taciturn.
1816   Remarks Eng. Mann. 61   The people in Europe who partake most with us in this taciturn propensity, are the Dutch.
1849   T. B. Macaulay Hist. Eng. II. vi. 68   Godolphin, cautious and taciturn, did his best to preserve neutrality.
1876   J. S. Bristowe Treat. Theory & Pract. Med. ii. vi. 852   The patient becomes apathetic, morose or taciturn, or irritable.

So if someone is laconic, he's not against communicating. He's about a certain style of communication: concision. But if someone is taciturn, he's avoiding communication. Taciturn speaks more of a personality type, and not in a good way.