Pedantically speaking, as soon as something happens, it's history. The seconds tick on, and it's there. Practically speaking, current events become history almost immediately, but perhaps in a different way to what you're thinking of.

A problem I've noticed a lot of people seem to have is associating the present with the past. It happens a lot on some Reddit threads about social issues, where you'll see someone bring up historical occurrences(slavery, colonialism, invasions, archaic laws about beating your wife) and other commenters will dismiss them, usually with a phrase like "But that happened years ago, it doesn't matter now!" A lot of people know this isn't the case, and that events in the past do affect those in the future. Almost everything an historian studies will reflect this. A sociologist can tell you what the effects of discrimination a century after the events are. A psychologist will tell you about communal memory or trauma - where an event is remembered so strongly by later generations that it appears as if they were present for it.

So why does all of this matter to your question? Because a lot of history(at least the popular stuff that makes it into these sorts of books you're asking about) is the big events. It'll look at the atomic bomb being dropped, the Civil Rights Movement, the Civil War, and the labour movements. All of these events affected the way some or all of us live today. And all of those events together have a cumulative effect, forming a national identity, shaping societal views, and influencing the law.

To swing back around to my answer of immediately, general history books take in everything about their topic, and much of the time they'll finish up at the time of writing. This is because everything up to the time of writing is either influenced by, or influencing, something else. It's also because once a book is published, it's not going to be read once in the year of publication, and then tossed out(hopefully). It's going to be a repeatedly referenced resource, and as the reader finds themselves more distant from the date of publication, those events that were contemporary to the author's time will be pored over by other historians. That'll give the reader a far broader range of opinions to take in, to analyse, and to form their own opinion from.

For some examples, I've got Howard Zinn's A People's History of the United States, and Michael King's The Penguin History of New Zealand sitting next to me.

Zinn's A People's History is a better example. It was first published in 1980, and several revisions appeared between then and 2003, which is my copy. The final five chapters in the 2003 edition go from the days of Carter and Reagan in the early 80s, to a short 7 page chapter on the 2000 election and 9/11.

King's book is a popular history which isn't written for historians, but for the general public. It was published in 2003, and it covers up until the 1990s in its final chapter. It has an interesting section following that called 'posthistory', which looks at society in New Zealand in the late 90s, and I think that shows the difficulty even historians have some times in defining history.

Overall, most historians would agree that there are many connections between past and present, so trying to separate the two doesn't always work. Further, the connections can be very important in terms of being relatable and useful. A thesis or academic paper that is written about an obscure and isolated incident in the past might never be cited or referenced today. On the other hand, a study of the trends in government attitudes towards slaves in post-civil war America could be extremely relevant, given the modern issues presented by Donald Trump's administration, or prior to that, police brutality against minority communities.