Participant survey: is it necessary to design sampling I'd like to ask if there is a difference between these two options in survey design.
We are running a mentoring program and want to measure if the program helps through the participant survey.
Let's suppose the program served 1000 participants.
Option 1:
The survey was distributed to all participants and 100 filled out the survey. Out of the 100, 60 said the program helpful.
Option 2:
The survey was distributed to randomly selected 100 participants and all of them filled out the survey. Out of the 100, 60 said the program was helpful.
Currently, the program measures the user satisfaction using the option 1 and I'd like to recommend the option 2. I think the two options should be interpreted differently, but not clear what would be the advantage of the option 2.

I think you're correct to suggest option 2, even though you'd probably need a larger sample size. Note that there are other study designs that might be relevant to evaluating your program (e.g. randomized controlled trials, case-control studies), but  it's outside the scope of your question, as you just want to know the best pick between option 1 and option 2.
If the expectation of option 1 is ideally to get answers from all participants, this not a survey but a census with a 90% non-response rate. It will have participation bias and volunteer bias. Additionally, targeting all participants will increase survey fatigue for all of them, including those who don't answer your question(s), which will be a problem for future surveys.
On a side note, if these 1000 people are initially willing to participate in the program, but after some time 90% of them are not eager to share their opinion about it, it would make me question either the way the survey is communicated or the program usefulness (but I don't know the context of your program, so my comment about its usefulness is to take with a grain of salt; non-respondents may have a lot of other reasons than indifference or hostility not to respond).
If you just want 100 answers but still distribute the survey to all participants, e.g. if it's a voluntary online survey that you distribute to everyone and you close it once you get 100 answers, this is akin to convenience sampling. It will certainly have bias too, i.e. those able to answer the survey quickly probably don't have the same profile as others. For example, people with various family obligations or some social problems may overlook your survey, when they may be a subpopulation particularly affected by your program.
As you expect a 100% response rate with option 2, I assume that it would be mandatory for the 100 students to answer the survey (e.g. if committing to answer your survey is a prerequisite for enrollment in the program). So one advantage if it's mandatory is that it would reduce volunteer bias drastically.
You will also have the advantages associated to probability sampling, e.g. estimating sampling errors (see https://en.wikipedia.org/wiki/Sampling_(statistics)), but you will have to make sure 100 is a number of respondents sufficient to answer reliably the question you have, which may be not the case - and in this case, I'd bet it's not enough. See Sample size determination; you can also ask a separate question if you need help determining the correct sample size for your survey.
Another advantage of a survey vs. a census is that it may require less resources compared to distributing the survey to 1000 participants. Finally, even if it may increase survey fatigue for the surveyed participants, at least you'll avoid it for the whole population. That's what Fosnacht et al. suggest in How important are high response rates for college surveys? (2017), p.19:

Porter, Whitcomb, & Weitzer (2004) presciently forecasted over ten
years ago that decreasing costs associated with designing and
administering online surveys would make survey fatigue more prevalent.
As many colleges and universities struggle with this phenomenon
today, they may want to consider randomly sampling smaller groups of
students when administering surveys. Hypothetically, if the aim is to
collect 50 respondents for a reliable estimate, and your population is
1,000, a reasonable approach would be to randomly sample 200 students,
assuming a 25 percent response rate. The remaining 800 unsampled
students could be used for other research or assessment projects, thus
reducing survey fatigue and potentially increasing response rates for
all surveys being administered on campus.

