How does Contract salary work for a fulltime role

I recently received an offer from a early stage startup. But they told that that pay in contractual basis. when asked about the reason they told that it helps the company and employees to save tax.

How does it work? will it affect my future employment if I take this job? like if I join some other company will they accept that I was actually working fulltime.

The role is fulltime, but only the money transaction will happen as contractual.