Reception/Modem/Baseband topic

Hello,

I recently upgraded from Xperia Arc S to Samsung Galaxy S4 I9505.
I bought my device from Hong Kong, with HK firmware. After I opened the package I put my SIM inside,
the reception was not very good. I was instructed by the company to use GSM only since there is no
LTE network in Israel as of today.

I flashed a couple of ROMs since and today I am on MIUI v5 which is my favorite, the reception remains
the same in all ROMs, quite bad compared to my old Xperia Arc S.

I was wondering about basebands and modems, I have been watching those two names floating around
the forums quite a bit and I never got around to playing with those.

So my questions are as follows:
1. Is there a different between modem and baseband or are these two just different words that refers to the same thing?
2. Does changing a baseband/modem can help get better reception?
3. If the answer to 2 is yes, which one should I get?

Thanks,
Oded