You are partly right. Sporting muskets were more accurate than military muskets. (This had nothing to do with "earlier" vs. "later".)

This was not because they were hand crafted rather than mass produced (no muskets were truly mass produced, with interchangeable parts, until late in the musket era). Although more craftsmanship might have gone into sporting muskets, and this might have contributed to some of them (the more expensive ones) being more accurate, the main reason was that military muskets were deliberately made less accurate to reduce the problem of barrel fouling, while this was not a problem with sporting muskets.

Sporting muskets were often called "fowlers" (in the American colonies at least). A fowler was a smoothbore firearm generally lighter than a military musket. They were capable of firing various loads from "birdshot" like a modern shotgun, to bullets. The fowler was often more accurate than a military musket. This was because the bullets were cast to fit the barrel more tightly.

Military muskets were built to fire 50 or more rounds in an engagement, without the black powder fouling the barrel and making further shots impossible until the gun was cleaned. Black powder is very fouling, so this required a bullet somewhat smaller than the barrel so that the gun could still be loaded and fired after numerous rounds. These gaps between bullet and barrel reduced the accuracy of the gun. Military muskets were also generally heavier and more rugged than fowlers, and could be fitted with bayonets.

Fowlers, were designed to be used for hunting. It was likely that only a few shots at a time would be possible against game targets, then the gun could be cleaned. Therefore, bullets were cast with tighter barrel tolerances and fowlers were more accurate than military muskets.

Modern firearm enthusiasts who hunt with 18th century fowlers report them accurate to 60 yards against game like deer and bear.

Fowlers were imported to the American colonies in large numbers (The largest numbers being "trade guns" to sell to the Indians for furs) from France, Britain, the Netherlands and Germany, and were also made by American gunsmiths.

Fowlers were most often in .60 or .65 caliber. They were often used for hunting deer, and were particularly useful for hunting birds like turkey, pigeons or water fowl such as ducks or geese, when loaded with shot like a shotgun.

The fowlers were also used for defense, and by the militia, although some militia were equipped with military muskets instead.

The Minutemen being armed with fowlers, while the British Regulars were armed with military muskets, may have contributed to the success of the American sniping attacks on the British column as it retreated towards Boston after the Battle of Concord, at the outbreak of the American revolution. Fowlers were more accurate at longer ranges than military muskets.

It's still smoothbores firing ball bearings by igniting black powder right? In that case, no. It's not going to be more accurate. The mini-ball and rifling were the innovations when it comes to accuracy.