Know and understand the difference. While related and complimentary, the two are distinctly different and best defined through example.
Data integrity comes first, considering data structure and logical validity. For example, framing a simple spreadsheet as a database for your favorite recipes. Each row represents a recipe and each column indicates recipe data and metadata. If all columns require data and there exists data in all columns, we might assume that we have data integrity.
However, if upon further inspection we see ingredients in the Title column, multiple titles and duplicates in the Title column, and narrative text not related to temperature in the Temperature column we see that we have poor data quality.
This is an over-simplified example, but should serve to promote better understanding. For more information, search the many titles and topics on the subject. Or, contact me as I’m always interested to discuss the topic further!