Hi, I will try to make it clear with my concept of paired t test. Firstly you have to understand the concept of independent samples. The concept is that the two or more samples taken from the same population do not influence in anyway the selection of subjects or participants in any samples.

If they influence then it become related samples. Whenever the samples are related you can used usual statistical test as they have assumption of independence of samples.

Having said that, if you have samples and you are measuring it twice on quantitative variable the test used will be paired 't' test ( second statement of yours) ( easy to understand). Now if you are doing one to one to matching the samples becomes related, in this situation also you have to use paired 't' test.

I hope it becomes clear now

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reading the following might help :

https://blog.minitab.com/blog/adventures-in-statistics-2/understanding-t-tests-1-sample-2-sample-and-paired-t-tests

"Many people are confused about when to use a paired t-test and how it works. I’ll let you in on a little secret. The paired t-test and the 1-sample t-test are actually the same test in disguise! As we saw above, a 1-sample t-test compares one sample mean to a null hypothesis value. A paired t-test simply calculates the difference between paired observations (e.g., before and after) and then performs a 1-sample t-test on the differences."

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Thank you Arun and Fabrice for your response and the blog link. It is really useful but I still have a doubt. Let me provide a scenario below;

For instance, I have administered pre- survey of 100 students and based on the findings of this pre-survey, I have implemented some intervention programmes and administered post-survey from the same 100 students to check if the intervention has made any impact. Is this suitable for a paired-samples t-text?

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yes because you will measure the effect of your intervention for each student individually (as a pre-post difference), which leads to a set of differences (100 values, one difference per student) and a standard null hypothesis of no effect (zero mean) ; at this point, you're back to a standard t-test

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yes. it is suitable to do paired 't' test in your case.

The basic idea of paired sample t test is two comparable scores are paired for the same individual

my understanding is paired sample t-test is within the same group. For example comparison of pretest and posttest scores within same group to p value or level of significance.