What is the difference between model.to(device) and model=model.to(device)?

Citing the documentation on to:

When loading a model on a GPU that was trained and saved on GPU, simply convert the initialized model to a CUDA optimized model using model.to(torch.device('cuda')). Also, be sure to use the .to(torch.device('cuda')) function on all model inputs to prepare the data for the model. Note that calling my_tensor.to(device) returns a new copy of my_tensor on GPU. It does NOT overwrite my_tensor. Therefore, remember to manually overwrite tensors: my_tensor = my_tensor.to(torch.device('cuda')).

Mostly, when using to on a torch.nn.Module, it does not matter whether you save the return value or not, and as a micro-optimization, it is actually better to not save the return value. When used on a torch tensor, you must save the return value - seeing you are actually receiving a copy of the tensor.

Ref: Pytorch to()

No semantic difference. nn.Module.to function moves the model to the device.

But be cautious.

For tensors (documentation):

# tensor a is in CPU
device = torch.device('cuda:0')
b = a.to(device)
# a is still in CPU!
# b is in GPU!
# a and b are different 

For models (documentation):

# model a is in CPU
device = torch.device('cuda:0')
b = a.to(device)
# a and b are in GPU
# a and b point to the same model