It depends on how you look at ‘inheriting’ and ‘borrowing’.
Allow me to start off by quoting from ScotM’s comment above:
I would say that the inheritance is a discrete form of one generation borrowing from a former generation.
This is arguably a logical way of looking at it: after all, we all acquire language by emulating others and using words that we hear others use around us, and in that sense, we all do in a way ‘borrow’ our entire lexicon (and grammar) from others. I would argue, though, that acquisition would be a better term for this.
In that case, inheriting and borrowing become two distinct ways of acquiring new words (two more are deriving and inventing), which I personally think makes more sense. The difference between the two is simply whether we acquire the word as a word in our own language from the community of speakers that we acquire our lexicon and grammar from in general (inheriting); or whether we acquire it from speakers of a different language as a word in a different language (borrowing).
That’s usually a relatively easy distinction to make, though there are of course many cases where you learn a word as a word in your own language by hearing it used all around you; but you and everyone else is still aware that the word is native to a different language (like, say, smorgasbord in English). Still, I would say English speakers who learn the word smorgasbord from their linguistic community nowadays are inheriting an English word, because they are not taking a Swedish word out of its native context in Swedish, as heard used by Swedish speakers, and applying it to English: they’re simply using a word that their own, English-speaking community uses when speaking English.
Contrast this with a scenario like the expat community in China, where certain Chinese words are in frequent use, but always with the distinct knowledge that these are local, Chinese words that are currently being added to the variety of English spoken in that community—they are not words used by the wider English-speaking community, and speakers are still acutely aware of their Chineseness. For example, when taking pictures, many foreigners living in China take over the Chinese practice of saying 茄子 qiézi ‘aubergine’ instead of ‘cheese’; but they do so knowing that they are ‘humouring’ the local practice, and that when they’re not in China, they should say ‘cheese’, which is the inherited picture-taking word.
(There are grey areas as well, of course: ‘language’ is notoriously ill-defined, and dialects and sociolects constantly borrow from each other as well—but is it really ‘borrowing’ when Brits start to use apartment instead of flat more and more commonly, for example?)
That’s looking at it from the perspective of each individual user of a language ‘borrowing’ or ‘inheriting’ a word. Another perspective is from the language or the word itself, and that’s different. The history of each word in a language goes back much, much further than any individual speaker (excepting brand new words, like fleek, which have not been part of the English language very long at all), and it makes sense and is useful to make a similar distinction between inherited and borrowed words in the language as well as in each individual speaker.
The difference is that once a word is borrowed into one language from a different language, its status will always be ‘borrowed’. Once its been in the language for a while, new speakers learn the word in an inhereted manner, and from their point of view, it will be an inherited word; but from the viewpoint of the language itself, it was borrowed at some point, so it’s still a loan word in origin. This is similar to how migrations work in many places: you may have been born in a particular community, but your great-grandparents moved there from somewhere else, so you’re still a blow-in, as our Antipodean friends call it.
Of course, the further back in history you have to go to see the borrowing, the less sense it makes to call something a borrowing. Nobody will think it odd to call smorgasbord or joie de vivre loan words, both being still quite un-English sounding and having been part of the English lexicon for only a bit over a hundred years. But some may find it strange to consider get or egg loan words, though they were borrowed (from Old Norse) no more than a millennium ago. And even most linguists will find it a stretch to call seven a loan word in Modern English, though it is almost unanimously accepted that Proto-Indo-European borrowed the word (*septḿ̥-) from Proto-Semitic some five or six thousand years ago.
Even so, there remain a group of words that do not, at any stage of the language that we have any kind of access to (i.e., back to Proto-Indo-European), appear to have been borrowed from a different language; words that have been acquired by speakers of the language stages that led up to Modern English entirely through inheriting, never through borrowing. These are the words that historical linguists call truly inherited words.