How to identify and differentiate frequency and time in EEG data using python?
It is hard to answer your question, since you do not seem to have experience with EEG data and/or general signal processing.

You say, your data is sampled at 200 Hz, which seems good to me for EEG data. 


What does it mean by sampling in EEG data? 
That means, that the (continous) EEG signal is choped up into discrete values. This is always necessary for further signal processing with computers.
I am getting the sample rate and the frequency when I plot the data as shown below. Shouldn't it be the time and frequency?


I don't know what you mean by I am getting the sample rate and the frequency when I plot the data. You certainly don't. The sampling rate/frequency is a fixed number given by your experimental hardware. You don't get it from your data - you have to know it from your experiment to get meaningful results from your data.

I also don't know what Shouldn't it be the time and frequency? means. Your EEG data is certainly a voltage signal over time, hence you have a signal in time domain.

Your sampling rate is given from your experimental settings and is 200 Hz as you say. Hence, each time point is separated by $$\Delta t = \frac{1}{f} = \frac{1}{200\,\textrm{Hz}} = 5\,\textrm{ms}$$

Your total signal that you have plotted is therefore $$4097 \times 5\times 10^{-3}\textrm{s} = 20.485\,\textrm{s}$$
long.

That is what you know from your data. Any further data extraction is up to you or your research question. If you'd like to get the frequencies that are in the signal, try to Fourier-transform it and extract the frequency region that you are interested in. As I see it, you have some apparent frequency components at approx. 13.4 Hz, 57.7 Hz, 81.0 Hz, and 88.0 Hz. Probably you are only interested in the lower spectrum around 13.4 Hz...