Re-running a trained network

Does re-running an already trained(run ) network affect the accuracy? if so why is it affecting it? so to be specific, I was running an image classification network, and I run the trainer part of the code and was just wondering and just re-run the same part of the cell(in google colab) and the accuracy was changed from the previous run by a bigger number( that is in the first run, the accuracy was around 45% ~ 50% in half of the epoch and reached around 68% in about 50 epochs but in the second run, the accuracy was 68% throughout the whole epoch of running)? so what is really happening there, is it like the network is saved or sth else? thank you

No, it will not affect the accuracy unless you keep the model in .train() mode and are thus updating e.g. the running stats of batchnorm layers etc.
As long as no gradients are computed and no weight updates performed, the accuracy of the model will not change.