OP wrote:
"I was using iPhoto. They are there inside the application."
I think what you need to do is this:
First, I would recommend that you use either an external USB hard drive or a USB flash drive to "move over" the files. Either one will work provided it's large enough.
Then, do this:
1. copy the "iPhoto Library" from your home folder on the OLD Mac to the "transfer drive"
2. Power down the old Mac and disconnect the external drive. Connect it to the NEW Mac and let the icon appear on the desktop... but...
3. DON'T open the drive icon yet.
4. Click ONE TIME on the external drive icon and type "command-i" (eye) to bring up the get info box for the drive.
5. At the bottom of the box there's a lock icon. Click it and enter the password you're using on the NEW Mac.
6. In the sharing and permissions area, there should be a checkbox "ignore ownership on this volume". Put a check into that box, then close the get info box.
THE ABOVE IS IMPORTANT to prevent permissions errors between your old Mac and your account on the new one.
Now you need to open a couple of folders:
- On the external drive, open your old home folder, so that you can see the "iPhoto Library".
- On the NEW Mac, open your home folder so that you can see the Pictures folder, but don't open it.
- Now, "drag and drop" the iPhoto Library file over the Pictures folder, and "let it go".
- You should see a dialog asking if you want to replace the existing folder with the new one. YES, you want to do this.
WARNING: this presumes that if there's an iPhoto Library on the New Mac, that you don't need to save anything in it.
The iPhoto Library from the old Mac should replace the copy that was there.
BUT WAIT... THERE'S MORE!
If you have a new Mac,
the older versions of iPhoto won't work with it any more.
New Macs come with Photos (instead of iPhoto).
Do you want to keep using iPhoto, or will you be using Photos?
Let us know what the answer is.
The ONLY VERSION of iPhoto that works with El Capitan, Sierra and High Sierra is version 9.6.1.
It can be "tricky to get ahold of".
I suggest you print this reply out and keep it handy.