The response rate would be the number of people who completed the survey divided by the number of surveys sent out. The completion rate would be the number of people who fully completed the surveys divided by the number of people who participated in the surveys but did not fully completed them.
Based on survey studies I have read, authors usually report the response rate but I rarely see the completion rate reported.
I am aware about this difference but the main problem that I have faced when reading survey studies is that some researchers referred to a completion rate as a response rate. In another word, some researchers have not differentiated between both terms. This issue have made me confused about the difference between both of them.
The term I've seen used for response rates for individual questions on a survey is generally stated in terms of nonresponse, and is called "item nonresponse." You could state the item nonresponse rate for each question, and the response rate (or more consistently, nonresponse rate) for the completed surveys. If you put that information into a table, that might be helpful in clarifying the situation.
Aside: It might be useful to note the order of the questions. Do the higher item nonresponse rates occur with the latter questions because the respondent thought the form too long and quit?