I want to know if there is a difference between "in the past year" and "during the past year".
𝗣𝗮𝘀𝘁 is used to refer to a period of time before and until the present.
We use the present perfect tense with time expressions - this year, in the past year etc.
I have seen her four times 𝗶𝗻 𝘁𝗵𝗲 𝗽𝗮𝘀𝘁 𝘆𝗲𝗮𝗿.
I saw her four times 𝗱𝘂𝗿𝗶𝗻𝗴 𝘁𝗵𝗲 𝗽𝗮𝘀𝘁 𝘆𝗲𝗮𝗿. ('during' refers to when this happened)
We usually use the simple past tense with 'during the past year'.
"In the past year" tends to refer to infrequent occasions and short periods of time while "during the past year" tends to refer to longer periods of time and more frequent occasions.
"Have you made any claims on your car insurance in the past year?" would suggest that the number of claims, if any, is going to be in low single figures
"Have you eaten in an upmarket restaurant in the last year?" recognises that, for most people, upmarket restaurants are a very special and infrequent treat.
"Have you been on many dates in the past year?" would indicate that the question was about one-off romantic encounters.
"What have you been driving during the past year" would suggest that the questioner was expecting the reply to be one vehicle, or perhaps two or three vehicles each of which had been owned for a number of months.
"Have you eaten out much during the past year?" would be referring to eating in ordinary establishments, possibly several time a week
"Have you had a girlfriend during the past year?" would be asking whether the other person had been seeing someone seriously over a number of weeks or months even if the relationship had ended.
These aren't hard and fast rules, however, just a tendency in those directions. The two phrases have a large overlap in their applications.