They have always been considered separate because the concept of a home computer didn't exist at the time video game consoles were first created. More to your point though, there has been crossover between the two, so I will explain this.

A computer in modern terms is a solid-state device than can calculate functions. Though there have been analog and electro-mechanical computers, this idea does influence the way that the term "computer" was used in early advertising for video games. The Odyssey, the first home video game device, never uses the term to describe itself. They preferred a broader idea of "electronic". However, Computer Space by Nutting Associates does use this phrase. It was actually inherited from a much older game, but in press for Computer Space, Nolan Bushnell specifically referred to it as a powerful computer capable of doing 25 million calculations a second. He was drawing on the idea of mainframe computers to sell this game.

In the intervening years, microelectronics allow computers to enter the home for the first time. However, it should be noted that the term "home computer" is not what these were referred to. The terminology of "home computer" specifically refers to computers that have a use in the home. Computers like the Altair 8800, Commodore PET, Apple II, and others were either "hobbyist computers" or "personal computers" more broadly. Only after this initial period did the idea of a "home computer" come into focus.

It was a marketing push of these early devices that there were uses of the computer for the average American. It could be an automatic bookeeper. It could replace a typewriter. Rather infamously among home computer historians was the gendered promise of "storing recipes" on a machine loading off of tape with 4K of memory... That was the really problem with the idea of a "home computer" industry forming. The computers could do basically nothing, had little software to support these ambitions, and paramountly were too expensive for any sort of average use. A TRS-80, the cheapest among the "fully assembled" early computers, was $599. That's a lot even for a middle class family in late 70s America.

There was from the start a stark division between what the general public saw as the utility of a personal computer versus a video game console. Check out this 1978 ad for the Apple II in which it says,

You don't want to be limited by the availability of pre-programmed cartridges. You'll want a computer, like Apple.

Take note of the use of the word "pre-programmed". This is because early users of microcomputers were expected to be - at least in part - programmers. Even interfacing with programs on these computers required a working knowledge of commands for loading. People fully recognized the separation in experiences between personal computers and video game consoles. The difference in the press as opposed to the public was how much value they put in the idea that computers were necessary to every person's future.

A number of early 1970s consoles attempted to expand into full computer capability. Atari had its Keyboard Controllers, the Bally Professional Arcade had a promised keyboard addon and BASIC programming language cartridge, the Odyssey2 was marketed as a "computer trainer", APF's MP-1000 had an expansion called the Imagination Machine which gave it expanded capabilities, and infamously Intellivision by Mattel marketed a computer expansion alongside the console. What all of these efforts had in common were that they were dismal failures, attempting to apply a strategy to marketing their systems as having greater value than "just" gaming devices. However, what they did was plant the seed of the idea of a "home computer" which would begin emerging going into the 1980s.

Once personal computers had sufficient capability to be able to display things like appropriately large lines of text, graphs, and have more operable I/O solutions, that's when the concept of the home computer took shape. By using the technology developed for - or to compete with - video games, the personal computer market could now sufficiently claim it was capable enough to be of real use to users. Plus, the prices came down dramatically. While early contenders in the home computer category like the Atari 400/800 and the TI-99/4 were expensive, soon enough the TRS-80 Color Computer (Tandy Coco) and Commodore's VIC-20 were being offered for $399 and $299 respectively. That then made it conceivable that most families could potentially afford a computer.

Side note: The reason that these prices came down has almost exclusively to do with new regulations set by the Federal Communications Commission in 1979. It's a bit complex, but basically they could be cheaper with their components and not have to provide as much shielding as they did previously. This act pretty much single-handedly enabled computer companies to drop the price of entry.

Comparing the Tandy Coco, VIC-20, and Atari 8-bits against the consoles of the day like the Atari VCS, Odyssey 2, and Intellvision, the difference in graphical fidelity is pretty minimal. There are some restrictions in how the games play, but functionally there was now a clear advantage to owning a home computer over a console. Commodore decided to be actively oppositional with ads featuring William Shatner which directly asked viewers a simple question, "Why buy just a video game?" This was a turning point. Now it was going to be on the video game companies to try and answer that question.

What should be noted: While the home computer industry was experiencing a rapid rise, it was nowhere near the sales of video game consoles. The VIC-20, released in 1980, was declared the first identified "computer" in history to sell over one million units in 1982. In contrast, Atari sold three million of their VCS consoles that year. The markets were not anywhere near each other in terms of success. However all the "hype" was propelled behind home computers, and people watching the industry started to ask the question if video game consoles even had a market niche. Why not just buy a home computer if it did the same thing and more at a comparable price?

The follow-ups of the major console companies in 1982 were almost universally-focused on providing a hybrid computer-console experience. Atari used their 400/800 technology as the basis for the 5200 system. Mattel released its own home computer, the Aquarius, and its Intellivision follow-up was meant to be fully computer-functional. Magnavox wanted the Odyssey 3 to be a fully realized vision of what the Odyssey 2 had been trying to be in 1978. Coleco raced to introduce its Adam computer addon to the Colecovision, either purchasable as a standalone device or modifying the console itself. All of these console companies were terrified that if they did not claim a part of the computer market, they would not have any stake to technology any longer.