Both convergent and concurrent validity evaluate the association, or correlation, between test scores and another variable which represents your target construct. Here is the difference:
Concurrent validity tests the ability of your test to predict a given behavior. For instance, verifying whether a physical activity questionnaire predicts the actual frequency with which someone goes to the gym. You could administer the test to people who exercise every day, some days a week, and never, and check if the scores on the questionnaire differ between groups.
Convergent validity examines the correlation between your test and another validated instrument which is known to assess the construct of interest. In this case, you could verify whether scores on a new physical activity questionnaire correlate to scores on an existing physical activity questionnaire.
Here is an article which looked at both types of validity for a questionnaire, and can be used as an example: https://www.hindawi.com/journals/isrn/2013/529645/ [Godwin, M., Pike, A., Bethune, C., Kirby, A., & Pike, A. (2013). Concurrent and Convergent Validity of the Simple Lifestyle Indicator Questionnaire. ISRN Family Medicine, 2013, 1–6. https://doi.org/10.5402/2013/529645]
A book by Sherman et al. (2011) has a chapter which describes the types of validity you mention - which are also part of the 'tripartite model of validity.' You may be able to find a copy here https://www.researchgate.net/publication/251169022_Reliability_and_Validity_in_Neuropsychology
The reference for the chapter is
[Sherman, E. M. S., Brooks, B. L., Iverson, G. L., Slick, D. J., & Strauss, E. (2011). Reliability and Validity in Neuropsychology. In The Little Black Book of Neuropsychology (pp. 873–892). Springer US. https://doi.org/10.1007/978-0-387-76978-3_30]