A chicken biriyani is a chicken biriyani no matter you buy it from a roadside stall on a cart or from a authentic biriyani exclusive restaurant. Both places use same basic ingredients like basmati rice, chicken, chillies, onion, etc. But the way it is prepared, the other ingredients which goes into it, the hygiene level, health quotient, the ambience, the way it is served, the taste makes the difference between ₹50 and ₹250.
Same way, there are numerous parts which makes a smartphone, a smartphone. You have just mentioned the basic parts like - cpu, camera, display. That doesn't fully make a smartphone, so yes looking at the manufacturer is important. Different brands might use, different internal parts as per their pricing and hence the difference in prices. And some brands would buy parts in huge bulks so that they get huge discounts and cheap rates. For ex., Xiaomi accepts that they follow this tactic to get big discount from their suppliers. And some brands imports the parts and build smartphones from scratch. And some of them actually import prebuilt boards and just assemble the other things. Importing a part would cost less than importing a prebuilt board due to excise duty and taxes. There are numerous other factors which influence the pricing.
i would just suggest you to pick the brand which offers official service around your area. You shouldn't end up traveling long distance to fix your phone. After sales service is more important than the sales itself.