How is turning on File Vault different from logging on my computer with a Password?Please explain .

FileVault protects your data when your hard disk or SSD fails and needs replacement, or when you retire and replace your computer, or when your computer is lost or stolen.

Your password protects some of your data. FileVault protects all of it.

FileVault will secure your information when—for instance—you’re unable to erase your storage because your computer or your storage hardware is failing or failed. Your login password doesn’t provide that.

Mac is a multi-user computer, too. Which means you can have two or more separate logins (admin and standard user, for instance), or can have a guest login, or several family members with logins. The password authenticates who you are. The FileVault password locks and unlocks all of the data for all of the users logging into the Mac.

If you really do need to protect your computer from the NSA or from other other intelligence service, there’ll be other and larger security considerations.

HWTech wrote:

...A user account alone does not protect your data from a technical user.

Surprising this NYTimes article has a good explanation of the difference...

To emphasize what HWTech writes: “Technical user” here means using something as incredibly complex as a common Mac cable connected to another Mac—you may well already have this cable in your desk—and a widely-documented key combination at startup. This being the sort of thing that a ten year old can manage. Deeply, seriously incredibly complex stuff, connecting cables. Stuff well beyond the comprehension of mere mortals.

As for the folks at the NYT, they missed the whole “your computer storage may fail, and your computer will get retired” case. And you can't always wipe your data when that happens. Which for many of us is a vastly more common occurrence than how the NYT focuses that article. All computers get replaced. All storage will eventually and inevitably fail.

Encrypt your data. Enable FileVault.

If you don't use Filevault to encrypt the drive, then if someone else gets access to your computer they can read everything on the drive as the data is visible to anyone with physical access to the computer. If you encrypt the drive, then a person will not be able to see the data on the drive. A user account alone does not protect your data from a technical user.

Surprising this NYTimes article has a good explanation of the difference:

https://www.nytimes.com/2018/03/13/smarter-living/how-to-encrypt-your-computers-data.html

FileVault encrypts your disk adding a layer of protection that a login password cannot provide. If you need to protect your data from the prying eyes of the NSA or if you are employed by the NSA, then you use FileVault.