@nik8singh , you are talking about two different things -- one controlled by the IRS and the other by SSA ( Social Security Admin ).
For IRS, , specifically for F-1 admissions, the first time on F-1 gets a five Calendar years of "Exemption" from counting days present towards satisfying SPT ( Substantial Presence Test ). So in your specific case since you entered US on F-1 in 2013 ( I am surprised that you entered on 12/30/2013 and not on Jan 1st 2014 ), However , this would have meant that ( and barring any other influencing facts / circumstances ) you were on "exempt" status till 12/31/2017.
Now , because your status was adjusted to H-1B on 12/11 2017, your exempt status terminated on that date and you started counting days present towards SPT. Therefore during 2018 would have met the SPT and be a Resident for tax purposes ---taxed on world income.
at the end of 2023 ( 12/11/2023 ) your status was again adjusted to F-1 -- but now you are NO LONGER an EXEMPT status individual, so you are taxed on your world income , even as a student on F-1.
The FICA exception is not connected to immigration status --- if you are student / trainee etc. and working at the University/school and/connected entities, then you are immune from FICA.
Does that make sense ? Do you need more help on this ?
pk
