MacBook Air recognizes the external drive but when I try to open it tells me to update it

According to an article on the Western Digital Support site, Western Digital no longer supports the WD Smartware software.

https://support-en.wd.com/app/answers/detailweb/a_id/30039/~/wd-smartware-end-of-support

They say the application is "a utility with the ability to schedule automated backups at periodic intervals which will take place without requiring user input." If that's what it is, I don't think you need to run it to retrieve your pictures from the drive.

If you have been using this drive on a Windows PC, it probably is formatted using NTFS. "Out of the box", macOS can read files from NTFS volumes, but cannot write changes back to NTFS volumes. There are third-party drivers you can get to let a Mac read and write NTFS volumes, but if you are going to be working mostly with the Mac from now on, I would suggest copying your data to another drive (internal or external) that uses one of these formats:

• APFS – This is Apple's latest file system, designed with SSDs in mind.
• HFS+, a.k.a. Mac OS X Extended (Journaled) – This might be better for mechanical hard drives (HDDs).

Macs have a built-in backup utility called Time Machine. If you dedicate an external drive to Time Machine backups, Time Machine will automatically save multiple versions of updates to your files to that drive when it gets a chance.

There are also two third-party backup utilities that many Mac users have, and like:

Carbon Copy Cloner: https://bombich.com/

SuperDuper!: https://www.shirtpocket.com/

I've used Carbon Copy Cloner for a long time, and there are others who swear by SuperDuper! My advice would be to forget about WD Smartware, and move on to Time Machine and/or one of these "clone" backup programs.

That covers the basics with respect to filesystem differences, and replacing the end-of-life backup program. What to do about getting photos into your MacBook Air is a separate topic, as that has a lot to do with how specific photo applications – like Photos – and cloud services – like iCloud Photos – work.

With respect to your photos, how did you manage those on the PC?

There are two basic approaches towards managing photos:

Loose files. You are responsible for organizing photo files using {Windows/File} Explorer or the Mac Finder. Other tools, such as photo browsers and photo editors, work according to the directory structure you establish.

Database. An application organizes your photos for you. The application pulls the photos (or references to them) into its private database, and does not appreciate you messing around with the database, or moving the files that it references, behind its back.

I could be mistaken, but I believe that Photoshop and Adobe Bridge represent the "loose files" approach – whereas Lightroom Classic and Aperture represent the "database" approach.

By default, Photos imports copies of your photos into its internal database. Your access to the database is through the Photos user interface, the ability to launch other editing tools from within Photos, and the ability to Export your pictures as loose files.

If you were loading your Photos Library for the first time, I believe things would go something like this:

1. Decide which drive you're going to put the library on. If that's an external drive, hold down the Option key while launching Photos to get to the dialog for creating and selecting a new library.
2. Import your photos. If you're letting Photos copy them into its library on your internal SSD, or on a drive that has been formatted using APFS or HFS+, you can probably import directly from your existing NTFS drive.
3. If you want to use iCloud Photos to sync photos between your Macs / iPhones / iPads, select the photo library as the "system" Photo Library and turn on iCloud Photos. (You'll need enough space in iCloud to store a full copy of the library.)