The sea has been split. The Jews go through while the Egyptians are washed away. The passuk tells us in 14:31, "וירא ישראל את היד הגדולה...וייראו העם את ה' ויאמינו בה' ובמשה עבדו" - Israel saw the great hand that which Hashem had done to Egypt and the nation feared Hashem and they believed in Hashem and in Moshe His servant.
Did they not believe in Hashem prior to this? After all they saw HAshem do to get them out of Egypt, only now do they believe in Him?What is different now that we say they believed in Hashem rather than the blief they had before?
I suspect my rebbe Rav Gamliel Rabinovitch would say that why they did not have emuna before this is not what matters. Rather, he would say, if the Torah says they have emuna now and not before, after everything they have seen and experienced, how much more so would we be considered people without emuna and how much more do we need to work on improving our emuna.
To answer the question though, it must be a different level of emuna based on what they just saw in how Hashem took out His wrath and vengeance on the Egyptians, relative to what they saw before which was much less. This level of emuna is based on their fear of Hashem, as it immediately attributes it to that by saying "They feared Hashem and they believed...".
Prior to this they might have believed based on what they saw, but it seems like they did not have the yirah that they have now.