if (condition || condition) vs if (condition) if (condition)

I just started the project Euler and I already have some problems. why do these methods produce different results?

int sum=0;
for (int i=0;i<n;i++)
{
if(i%3==0 || i%5==0)
    sum+=i;
}

vs

int sum=0;
for (int i=0;i<n;i++)
{
if(i%3==0)
   sum+=i;
if (i%5==0)
   sum+=i;
}