What is the difference between SGD classifier and the Logisitc regression?
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SGD is a optimization method, while Logistic Regression (LR) is a machine learning algorithm/model. You can think of that a machine learning model defines a loss function, and the optimization method minimizes/maximizes it. 

Some machine learning libraries could make users confused about the two concepts. For instance, in scikit-learn there is a model called SGDClassifier which might mislead some user to think that SGD is a classifier. But no, that's a linear classifier optimized by the SGD.

In general, SGD can be used for a wide range of machine learning algorithms, not only LR or linear models. And LR can use other optimizers like L-BFGS, conjugate gradient or Newton-like methods.