I can do it using a laptop. But is there a way I can do it without passing them through a laptop each time?
In my understanding, I suppose that Photo Stream will do the trick.
Go to Settings > iCloud > Photos > My Photo Sream, and turn it on.
Enable iCloud on both devices using the same Apple ID, and you can see the latest photos in Photos.
If you want your photo library to be completely in sync across your devices, you need to use iCloud Photo Library. You'll need to be on iOS 8.3 or later on both devices.
Log into the same iCloud account on both devices, then go to Settings > iCloud > Photos, and turn on iCloud Photo Library. Go to the Photos app, make sure it's uploading, and then it'll take care of itself.
If you have more than 5 GB of photos, you'll have to pay monthly for iCloud storage. The cheapest plan is 50 GB for $0.99 a month.
If your devices don't have enough storage to hold all your photos, you'll want to select "Optimize [device] Storage", so only recent photos, favorites, and photos you look at often will be kept on the device. The others will be stored in the cloud, and they'll download when you tap on them.
If you don't want to ensure iCloud then you could simply try using AirDrop which is the most convenient way to transfer anything between multiple Apple devices
Enable iCloud on both devices using the same Apple ID. Make sure Photos is turned on with most of the options turned on (perhaps not "Upload Burst Photo's").