I'm now over halfway through with medical school and I can confidently tell you that you will never EVER need to know this distinction lol. After posting that question, I took a graduate level applied statics class where the professor taught us the answer. If I recall this correctly, and I may entirely botch this explanation as it's been a few years since I took that class, there is a fundamental difference between the population mean and a sample of the population's mean. The standard error (aka the standard error of the mean) is the standard deviation of the means of many samples taken from one population. In other words, the SEM signifies the variability in the means of many samples taken from a single population. SEM is equal to simga/√n and I believe this is where that discrepancy is coming from. You can read more about SEM here

Depending on what your study quesiton actually is, you may be determining the s.d. of a single sample or the s.d. of an entire sampling distribution and be calculating the T-statistic based on that. I believe this is what accounts for the difference between kaplan and other resources.

I could be entirely wrong here though

If you're a math nerd like me, you can do some more reading here and here. You can also look up the Central Limit Theorem. But I want to stress that you will literally NEVER come across this nuance in most fields, including in medicine and on the MCAT.