Part of it is our definition of cities versus metro areas. Boston's population is technically only 650k but Boston proper doesn't even include Cambridge which is like not including one of the boroughs when talking about NYC's population.
Granted, we still have a lot less metro areas with over 1 million people but there are still ~50 of them.
Is this something fairly unique to the US or do other countries do this too? that is, having a city boundary that's relatively small compared to the metro area.
I don't know if it's common to other countries, but a big factor in the US is race and class. There was a ton of "white flight" in the US starting in the 60s with white middle class and above fleeing cities to the suburbs. As such, they specifically did not want their adjacent town to be annexed by the major city.
In plays out pretty comically in Austin TX in my opinion. You have these teeny affluent enclaves (search for "Sunset Valley", "Rollingwood" and "Westlake Hills" near/inside Austin) that anyone else would consider "part of Austin", but they don't vote in city elections or pay city taxes (but they certainly take advantage of all the benefits of being close to Austin...)
In Spain it happens as well. The official city population numbers quoted by most sources are actually the population of the city's municipality. Sometimes municipalities are large, including rural areas and small towns close to the city, while other times they are smaller and leave outside areas that are effectively boroughs of the city (you walk down a street and are in a different municipality, without even going through any non-urban area). Some years ago there was a project to merge municipalities, focusing especially on cases like that, but it failed spectacularly because it required consent from all municipalities involved and the smaller ones never wanted to merge (partly because it's advantageous for them to not pay big city taxes but still use their services, but I suspect mainly because mayors don't want to just give up their position and go find another job).
This makes rankings by population rather biased and spawns many endless discussions on whether city X is bigger than its rival city Y (and sometimes it might actually have real-life consequences, say, when the central government comes up with some funds for cities of size greater than some threshold).
* How government is setup, in some countries (and in some areas of countries) many things are done at the city level, others bump a lot up to county, state, or even country government. The USA manages schools at the city or below, and so city boundaries become well-fought over.
Whenever you see "Unified" you're seeing something built out of smaller, usually city-related, parts.
The US went really hard on cars and single family housing. Without a lot of older cities in many places the surrounding land was cheap so people spread out (also due to racist zoning laws, “stimulating the economy”, general greed, etc it’s kinda hard to point to a single reason).
France does it too. Paris Proper has about 2 million people; the Paris metro area is about 10 million. China does it in reverse, they define a "city" which includes mostly farmland and rural areas, artificially upping city population figures.
Canada has/had that too. Eg: Montreal used to be a pretty small part of the Montreal metro until they merged all the cities on the island. Even then it doesn't include it's north and south chores.
Well, Paris is either very dense or not very depending on what arrondissements you're counting. London has The City, that doesn't even have many residents and then there's really the city core and greater London.
Granted, we still have a lot less metro areas with over 1 million people but there are still ~50 of them.