What is the difference between the words "airlines" and "airways" semantically?
This answer assumes that you are asking about the business name chosen by various air transport companies, such as "American Airlines" vs "British Airways".



Short answer:

There is no difference semantically. It's purely a marketing decision. The company decides which "sounds better", and uses that as their official business name. There are several other similar nouns used in business names as well:


"Air" (either before or after): Air France. Korean Air. Or even as part of the name: Ryanair.
"Aviation": Grant Aviation. 
And then don't forget that Delta uses a space:  Delta Air Lines. 
And then there are even some companies using several different nouns throughout their sub-divisions:  "Trans Executive Airlines of Hawaii" is the name of a single airline company, but their cargo services are performed under the name "Transair", and their passenger services are performed under the name "Interisland Airways"




Long answer:

There is some historical context, going back to the days when ocean travel was the only form of international travel between continents separated by oceans. A "line" was a route between two points. A "liner", then, was a ship that sailed that line. Since it was on the ocean, it was commonly called an Ocean Liner, and companies that popped up to provide a scheduled service on those lines used the term "line" or "liner" in their name: Black Ball Line, or American President Lines. 

When Trains came into being, they took up the same vernacular from their ocean transport heritage. The system of rails between two points was usually built by a company for its own use, and was sometimes called a "railroad", or a "railway", with no discernible reason why some chose one term over the other. The term "line" was still used, interwoven into the industry: a "main line" was a company's main route between two cities, and a "spur line" would branch off to a smaller town.  Some companies named themselves with either the "roads" or the "ways" part: The Kansas Pacific Railway, or the Western Pacific Railroad.

The next major transformation in the transportation industry was air travel, which again borrowed terminology from both its ocean and rail heritage. An "air line" was a route between two points, and an aircraft providing service on that line was an "air liner", and company names went one of two directions: Air Lines (such as "Eastern Air Lines"), or Airways (such as "Western Canadian Airways")

The terms "air liner" (for an aircraft) and "air line" (for a company) eventually worked their way into the single-word terms as we know them, and they are officially defined, today.

But even in the early days, there were still many different nouns working their way into the company names: National Air Transport, Western Air Express, or Ford Air Transport Service. Following the Air Mail Scandal, (in which existing companies had to give up their air mail routes), many companies either merged or simply changed their names to re-gain air mail contracts. Several companies with names of XXX Air Lines (with the space) simply changed to XXX Airlines (without the space), and this is now why we see this term (Airlines) in company names today.  (with Delta Air Lines being a notable difference)