First code does not pass all tests since there is no validation for total amount to drop below 0 spice collected.

            if (totalGathered < 0)
            {
                totalGathered = 0;
            }

When using any number below 26 this will result in a negative result in the final output, which is not a problem in the second solution because the final 26 spices get only subtracted inside of the while loop. 

Add the above validation to your first solution to fix the problem:

using System;
 
namespace SecondApp
{
    class Program
    {
        static void Main(string[] args)
        {
            int startingYield = int.Parse(Console.ReadLine());
            int days = 0;
            int totalGathered = 0;
            while (startingYield >= 100)
            {
                days++;
                totalGathered += startingYield - 26;
                startingYield -= 10;              
            }
            totalGathered -= 26;
            if (totalGathered < 0)
            {
                totalGathered = 0;
            }
            Console.WriteLine($"{days}");
            Console.WriteLine($"{totalGathered}");
        }
    }
}