Transformer core shape for IF application?
If I make transformer using different type of core, would performance be compromised?

Yes, that small shielded transformer on the PCB is used for (radio) signals. Note how it has a "screwhole", this is used to tuning the combination (transformer + other components on the PCB) to a certain frequency in order to filter out that frequency. The components for a resonant tank and are used as a Bandpass filter to suppress unwanted signals for example.

The yellow transformers are for power applications they're used in flyback power converters like power adapters. They're designed to turn electric energy into magnetic energy and back. Efficiency is key here.

The power transformers are not designed for resonating at a specific frequency, they're not tunable, they might be non-linear (harming your radio signal).

All in all, allthough they're both transformers of some sort they serve entirely different purposes and cannot be exchanged.