There is no particular reason why Louis Pasteur's germ theory of disease was formulated about the same time as the invention of the Gattling gun.In other cultures they might occur at widely separated historical periods.Broad tech classifications also encourage cinematic-style invention and gadgeteering — if you’re an Industrial Age mechanic you can fix anything from an early steamship to a World War II fighter plane.
Broad technology schemes cover centuries or millennia, and they describe a whole suite of interrelated technologies and social structures.This usually implies that cultures develop along a similar path.The convoluted way that tech advances influence each other was the entire premise behind James Burke's documentary series Connections and The Day The Universe Changed, which you should watch if you haven't already. The tabletop boardgame Civilization popularized the use of tech trees in 1980.And pretty much every 4x game uses tech trees, with the items accessed by investing in tech research."Technological advance is an inherently iterative process.Contrast Schizo Tech, Aliens Never Invented the Wheel, Sufficiently Advanced Bamboo Technology, Alternate Techline, Anachronism Stew and/or Fantasy Gun Control.
This has some actual reference in the real world Kardashev Scale (Note that when an interstellar colony is established, the tech levels can become scrambled due to the colony infrastructure problem (e.g., horses make more sense than automobiles if the colony has no oil wells to produce gasoline).
A much better model is the multi-branched "tech tree." The technology required to make an iron sword has the prerequisite of a supply of iron and a furnace to heat it.
Both of which require the technology of making fire.
An alien world with "Renaissance-era" technology (ignoring for the moment that the Renaissance spanned four centuries and giant changes in technology) in, say, firearms will also possess lenses, ships, building materials, and mathematical principles identical to those that Earth (read: the inter-continental trade powers of north-western Europe) possessed along with said firearms.
It's only rarely that a civilization will break off the path, and usually as a result of external forces providing them with something outside their capabilities (intentionally, accidentally or incidentally), such as a 1920s planet with fusion power, or a 1700s planet with radios.
Except, in this case the distant descendants of unrelated branches can inspire and influence the future of others.