Data science allows working around with data to get insights. It requires tools that are beyond machine learning like data analysis, slicing, and dicing the data.  Machine learning is a part of the data science based on the data for prediction. Both are somehow different, and it is your choice that you want to learn first. If you want to stick to machine learning, then no data science tools or techniques are required.  But if you work in the industry, then you have to have data knowledge first before going for machine learning techniques.