The simplistic answer is
Access is a personal database solution meant for small to medium size databases with a small user base and able to run on a personal computer. It was designed sufficiently to satisfy that scenario.
SQL server is a multiuser database solution meant for large databases with a large user base therefore far more effort went into maximizing its performance, some of which comes from running it on high end (and expensive) servers, in order for it to cope with that many users and that much data.
Quality assurance is all about making your product good enough to satisfy its purpose and no more. This is not to say that Access is an inferior product because it is not. Used in the context of what it is meant for it is a great product that is perfectly capable of delivering satisfactory performance.
As your data and/or your user base grows then it makes more and more sense to invest in a high performance database such as SQL Server.
What did the developers of SQL Server do differently than the developers of Access?
I understand this is a fairly open-ended question but I've struggled to find distinct reasons why it is such a superior method of data management other than "because it's just so much better, look at the stats!"
Microsoft aren't going to give away their secrets to their competitors.
They will only give enough info to prove their argument and in the end, the exact "how?"
doesn't really matter.