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In second approach you can eliminate usage of boolean flag, and condition check in second while loop. Also with some comments this code becomes easier to understand:

public static int GetWordsCount(string text)
{        
    int count = 0;

    for (int i = 0; i < text.Length; )
    {   
        // process to next word 
        while ((i < text.Length) && (text[i] == ' '))
            i++;

        if (i < text.Length)
            count++;

        // loop till the word end
        while ((i < text.Length) && (text[i] != ' '))
            i++;            
    }

    return count;
}

public static int Wordcount(string strName)
{
    bool wordfound;
    int ctr = 0;

    for (int i = 0; i < strName.Length; )
    {
        wordfound = false;

        while ((i < strName.Length) && (strName[i] == ' '))
            i++;

        while ((i < strName.Length) && (strName[i] != ' '))
        {
            if (!wordfound)
            {
                ctr++;
                wordfound = true;
            }
            i++;
        }
    }

    return ctr;
}

public static int GetWordsCount(string strName)
{
    bool wordfound;
    int ctr = 0;

    for (int i = 0; i < strName.Length; )
    {
        wordfound = false;

        while ((i < strName.Length) && (strName[i] == ' '))
            i++;

        while ((i < strName.Length) && (strName[i] != ' '))
        {
            if (!wordfound)
            {
                ctr++;
                wordfound = true;
            }
            i++;
        }
    }

    return ctr;
}

Also you don't need second if. If char is not white space, then it white space. And improve naming - don't use prefixes for variable names.

For me its a little harder to understand, because you are incrementing loop variable in loop body on some conditions inside other loops. But you are not creating strings here as you do in your second approach. So it's definitely better in terms of performance and memory usage, than you original second approach.

Also you don't need second if. If char is not white space, then it is white space. There is no third option. And improve naming - don't use prefixes for variable names.

For me its a little harder to understand, because you are incrementing loop variable in loop body on some conditions inside other loops. But you are not creating strings here as you do in your second approach. So it's definitely better in terms of performance and memory usage, than you original second approach.

But of course its better to use already existing functionality:

return text.Split(new[] { ' ' }, StringSplitOptions.RemoveEmptyEntries).Length;

Its not that fast, and it creates array of words which uses memory. But it's easy to understand for other developers. So, instead of doing premature optimization, I'd go with this approach and modified it only in case of performance problems.