Some methods:
iCloud Photos
If your devices are logged into the same Apple Account, you can use iCloud Photos to synchronize their Photos libraries. All of your photos and videos are stored both in iCloud ("on Apple's servers"), and on all devices that synchronize against iCloud.
Set up and use iCloud Photos - Apple Support
Note that since iCloud Photos is a synchronization service, deleting a photo in one place deletes it everywhere. However, you can save space on individual devices by using the "Optimize … Storage" option. This allows the devices in question to store lower-quality, space-saving copies of your photos and to fetch full-size copies on demand. (The choice of when to do substitutions is completely automatic; you have no control over it.)
A Mac can have several Photos libraries, in which case at most one (the "system" library) can be connected to iCloud Photos. The others are strictly local to the Mac and can be used to store pictures that you do not want stored everywhere.
Create additional photo libraries in Photos on Mac - Apple Support
Importing photos from an iPhone or iPad to a Mac or PC
This article mentions iCloud Photos, but also mentions some other possibilities (like importing selected pictures from the iPhone to a Mac's Photos library, or using Image Capture). If you have a third-party application such as Adobe Lightroom Classic, it also might have mechanisms for importing photos.
Transfer photos and videos from your iPhone or iPad to your Mac or PC - Apple Support
Manual synchronization from a Mac or PC to an iPhone
Sync your iPhone, iPad, or iPod using your computer - Apple Support
Note that manual synchronization might load your iPhone with lower-quality space-saving versions of your photos. This behavior started way back in the iPod days, before there was any such thing as an iPhone. At that time, iPods had very little storage, and very low-resolution screens, compared to today's iPhones, and couldn't have displayed anything like the detail in a full-size photo file even if one was willing to waste the space needed to store it.
Copying photos between Macs
Export photos from the first Mac's Photos library, copy the files to the second Mac, and import them to its library.
Note that Photos can store an original photo and an edited version together as "one photo". If you export photos, you'll need to choose which version (original or edited) to export. I don't know if there's any good way to transfer "the whole package."