With phonetical search, you have the freedom of spelling the Arabic words your way, using the familiar English alphabet and submit them for search. 

The  errors that might be present in your spelling are tolerated, corrected and then searched within the Holy Qur'an. 

Example.  Muhammadun Rasululullah, Mohammadurrasululullah, Muhamadun Rasoolulullah...    

Phonetical search presented here is performed towards the Arabic Qur'an. Thus, it should not be mixed with the English Translation searches. Submitting English words into phonetical search algorithms will never yield correct results. 

For English Translation searches, you may use this page.   

What does phonetical search have to offer ? Any advantages over the conventional searches ?  

A conventional search is performed within the same language. On the Internet, most of time, this yields itself as an (English-English) directed search. 
But needless to say, this type of search never allows the true searching of the Holy Qur'an. All it allows is to search the translations. The greatest drawbacks with this are the following; 

Searching a translation reliably depends on the unlikely hope that the translator interpreting the Quranic words the same way you do. 

For example, consider the word "Jannah" ( which is the corresponding Arabic word for "paradise" ). 
We know from the existing works that the translators interpret the same words differently ( depending on the context of the ayah ). 
And as a result of this phenomena , the example "Jannah" may come in the form of not only "Paradise" but also in the forms of "heaven" or "gardens". It is obvious that a search performed this way is not to yield true compilation of all the verses that contained "Jannah" in the Holy Qur'an.

The second drawback with an English to English search is that, it is not possible to find the reference(s) of those specific verse(s) which you happen to remember the exact phrases from. ( Ex. Amanar rasoolu, Kul huwallahu ahad, La ila he illah ). And in deed, many times, you may want to locate the Arabic phrase | verse from what you remember.

With the phonetical search however , these issues can be brought down to minimum. With the error tolerant phonetical search algorithms, one can conveniently type an Arabic word or a phrase in the most natural way. And this is done using the very familiar characters in English alphabet from that is A to Z.

What can be done with the phonetical search ?

This program can be used as a Qur'anic study and research tool. 

For example, compiling all the verses which contain the phrase "Yaa ayyuhallathina aamanoo" ( O you who believe ! ) can be perfectly and reliably queried. This would give the researcher the very dependable list of those versus where Allah (swt) addresses the Believers in the most direct way. The search is dependable as it is performed against the computer generated transliteration of the Holy Qur'an. 

"Allahu  yuhibbu" means "Allah loves". Knowing this, one then can simply submit the phrase "Allahu yuhibbul" and see what does Allah (swt ) love the most ?
Similar study can be conducted on "Allahu la yuhibbu" which means "Allah does not love". 

Ever wondering how many times the prophet (swt ) addressed by Allah ( swt ) ? Just submit "Ya ayyuha alnnabiyyu" and see for yourself.