Push feed and controlled feed are two different bolt action designs. The main difference between them is how the cartridges are fed into the chamber.
A push feed bolt action rifle uses a simple mechanism to push the cartridge from the magazine into the chamber. The bolt has a small lip on it that engages the rim of the cartridge and pushes it forward. Once the cartridge is in the chamber, it is held in place by the bolt. The push feed design is generally considered to be less reliable than controlled feed. As it is easier for the cartridge to be double fed or jammed in the mechanism.
Controlled feed bolt action rifles, on the other hand, have a more sophisticated mechanism that ensures the cartridge is properly aligned and fed into the chamber. In this design, the bolt extractor claw engages the cartridge rim as it is fed from the magazine into the chamber. This helps to ensure that the cartridge is properly aligned and securely in place before the bolt is closed. As a result, controlled feed bolt action rifles are therefore considered to be more reliable than push feed designs. This especially true under harsh conditions or when using cartridges with high pressure or heavy recoil.
Basically, the main difference between push feed and controlled feed bolt action rifles is the way in which the cartridges are fed into the chamber, with controlled feed being more reliable due to its mechanism for properly aligning and securing the cartridge.