To me, the first one implies that, for example, you invited a person out and you chose a place to go. Most likely a place that the person you invited has never been before. ANd the chances that they will like where you are taking them is pretty high. ->An example: "I'm taking her to this comedy show later this week but I hope she won't think it's boring" "I'm sure she will be interested, don't worry, just have fun!" The second sentence seems to imply that you have not asked anyone one out (yet) but maybe you are planning to. it could also just be somebody asking about another person interests. -> Heres an example: "Do you think she would enjoy going to a jazz cafe with me?" "I'm sure she would be interested!" Just another point... "Would" is a modal verb. A modal verb is "used to indicate modality – that is likelihood, ability, permission, request, capacity, suggestions, order, and obligation". Simply put it is a kind of verb that express probability in a sense. So, in essence, the sentences do with the same thing but the nuances are different. In the first one, the question implies that she has already agreed to go somewhere with you. The second implies that she has not agreed to go anywhere with you. As such, another way the second sentence could be written is as follows: "IF you ask her out, I think she would be interested" (<- In this sentence, there is an emphasis on the "if") I hope this helps! Good luck in your language endeavors!

There is a difference between will and would. The first one is used to talk about the future, while the second one is used to talk about the past. https://learnenglish.britishcouncil.org/english-grammar/will-or-would this is a great explanation😊