The Islamic Calendar is a purely lunar calendar, whereas the Hindu one is the LuniSolar calendar. Means we add an extra month every three years or so. It's like having two March back to back. So, our New year comes around in March, April every year. Whereas Ramadan (start of Muslim New Year) based on pure lunar cycles coincidently started with the same date as today is the start of the waxing moon cycle.

But the Ramadan date will shift through each year and with every year they will get like 12 days behind, 22nd March in 2023, 10th March in 2024 and so on. And that is the drawback of the pure lunar calendar.

p.s. Hindu New Year in 2030 is on 3rd April (source - my Hindu Calendar app)
Ramadan in 2030 is on 5 Jan (google)

As far as I know, the birth of jesus used the Gregorian calendar, if that makes sense?

Not sure what you mean there. I am not familiar with Gregorian Calendar's history.