This question itself looks strange that Dawah is needed for Muslims/Non-Muslims.
Da‘wah or Dawah (Arabic: دعوة) denotes the preaching of Islam. Da‘wah literally means “issuing a summons” or “making an invitation”, Tabligh literally means ‘to convey’. Contextually, it refers to conveying the message of Islam.
In Islamic theology, the purpose of Da‘wah is to invite people, both Muslims and non-Muslims, to understand the worship of Allah as expressed in the Qur’an and the sunnah of the Prophet S.A.W. Invitation may be of Emaan/Person Having Emaan but to strengthen it or/of Amal e Saliha.
In the word of Maulana Saad Damat Barkatuhum Dawah of Islam is for Non-Muslims and Dawah of Emaan is for Muslim. There is a misunderstanding that Dawah is not for Muslim
Those who are raising issue Dawah to Muslims/Non Muslims are simply cofusing General Muslims on different terminologies.
DAWAH CALLING TO ALLAH INVITING WAY OF ALLAH TABLIGH
There literal meaning are different. In literature they but all of these responsibilities were carried by prophet under the broad ambit of Dawah. So differentiating these term is OK for Literally Purpose, but at ground these term are alike.
Unfortunately some Muslims are becoming tools for spreading confusion and misunderstanding these terminologies.
May Allah save all of us.
Some Examples of Dawah Among Muslims.
1.Allah Talla Himself give Dawah to Muslim in Quran. Both these Ayats are for Muslim.
YA AIUHAL LAZINA AMAnud khulu fissilme Kaffah……………………
O the believer enter into deen completely
Ya Aiuhallazina Amanu Aminu………….
O the believer, believe……….
1. Adhan is five time Dawah for Muslim that has been called as Dawatut Tammah. (Complete Dawah). It is not for Non Muslim but Muslims.
2. Masab Bin Umair R.A. was sent for one year for those who accepted Islam. Rather Sahaba requested for it.
4. 70-80 % Muslims (at some places) are not even performing the foremost command Salat/Namaz and others command.
So it is much needed now a days that Dawah work with all might and effort to be done Both among Muslims and Non Muslims.
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May Allah help you.