If I understand your post:
Your question can be framed as a repeated measures analysis.
This is also called a within-subjects or within-respondent analysis.
The same respondent was asked the same question under two conditions.
As framed there is no second group of respondents. So the analysis is for the SAME people.
2 groups measured on one variable ==> ordinary t-test
1 group measured twice on one variable. (twice can refer to two time, or two conditions such as a variation in the stimulus question, etc).
Art Kendall
Social Research Consultants