I concur with everything Jake said.
Apple is encouraging people to use "iCloud Photos" instead.
"Instead" is a misnomer in this instance. With My Photo Stream, you could arrange things such that it automatically synced between iPhone and the Photos app on your Mac - in such a way that you could subsequently discard any pictures on your iPhone without losing any pictures on the Mac.
I have done that that for years.
iCloud Photos is really very different. It syncs your pictures from iPhone to Mac, BUT, add or delete a picture on the iPhone and it will add or delete that picture on the Mac - and vice versa.
I have 20K pics and videos in my Mac's Photos Library. I do NOT want 20K pics of the same on my iPhone!!
Apart from the difficulties of sorting this amount of data, many iPhones do not have enough storage space!
So, I have, as Jake said, to manually import pics & videos from my iPhone to my Mac.
You will need some form of BU for your Mac's pics/videos. You could pay for iCloud Storage by ticking iCloud Photos within the Preferences section of the Photos app - OR - use Time Machine and/or a cloned BU (I use both)
Another difference between My Photo Stream and iCloud Photos is that with iCloud Photos, they are stored in the Cloud at your expense! So if you have 20 thousand pics/videos like me, it will cost you to keep them in iCloud. Granted, the charges are not exorbitant - £$2-49/month for 200GB of iCloud storage - that is for ALL things stored in iCloud, not just your pics/videos.
So, I agree entirely with what Jake said - use Image Capture (Free app in Finder > Applications) to transfer the pics etc to your Photos Library (or to anywhere on your Mac for that matter).
Lastly: Image Capture is a fast and user-friendly way of deleting large numbers of pics/videos FROM your iPhone should that be necessary. The trick is to attach the iPhone to the Mac by cable, identify the pics/videos by clicking on the iPhone on the left. Now, Click on the top picture to highlight it.
Then - if you want to delete ALL your pics/videos - use Command A to select them all. Then RIGHT Click on any pic and choose Delete and All. This saves tons of time if you try to do it manually.
If you only want to delete SOME pics/videos, then hold down the Command key and scroll through your collection with the mouse and Left Click on each one you want to delete. When finished, Right Click on any one and, again choose Delete.
HTH - but actually Jake said most of this in his post.
Ian