How do I distinguish between generic and non generic signatures using GetMethod in .NET?

Don't use GetMethod, use GetMethods, then check IsGenericMethod.

using System;
using System.Linq;

class Program
{
    static void Main(string[] args)
    {
        var mi = Type.GetType("X").GetMethods().Where(method => method.Name == "Y"); 
        Console.WriteLine(mi.First().Name + " generic? " + mi.First().IsGenericMethod);
        Console.WriteLine(mi.Last().Name + " generic? " + mi.Last().IsGenericMethod);
    }
}

class X
{
    public void Y()
    {
        Console.WriteLine("I want this one");
    }
    public void Y<T>()
    {
        Console.WriteLine("Not this one");
    }
}

As a bonus - an extension method:

public static class TypeExtensions
{
    public static MethodInfo GetMethod(this Type type, string name, bool generic)
    {
        if (type == null)
        {
            throw new ArgumentNullException("type");
        }
        if (String.IsNullOrEmpty(name))
        {
            throw new ArgumentNullException("name");
        }
        return type.GetMethods()
            .FirstOrDefault(method => method.Name == name & method.IsGenericMethod == generic);
    }
}

Then just:

static void Main(string[] args)
{
    MethodInfo generic = Type.GetType("X").GetMethod("Y", true);
    MethodInfo nonGeneric = Type.GetType("X").GetMethod("Y", false);
}