What are the differences between sadaqah, infaq and wakaf?
Alhamdulillah, praise and gratitude to Allah SWT for His countless blessings for us all. Praise and salutations to our beloved Prophet Muhammad PBUH, his family, companions and all those who follow his footsteps until the Last Day.
Sadaqah includes the meaning of the obligatory zakat and sunnah donations as meant in the Quran:
إِنَّمَا الصَّدَقَاتُ لِلْفُقَرَاءِ وَالْمَسَاكِينِ وَالْعَامِلِينَ عَلَيْهَا وَالْمُؤَلَّفَةِ قُلُوبُهُمْ وَفِي الرِّقَابِ وَالْغَارِمِينَ وَفِي سَبِيلِ اللَّهِ وَابْنِ السَّبِيلِ ۖ فَرِيضَةً مِّنَ اللَّهِ ۗ وَاللَّهُ عَلِيمٌ حَكِيمٌ
“Zakah expenditures are only for the poor and for the needy and for those employed to collect [zakah] and for bringing hearts together [for Islam] and for freeing captives [or slaves] and for those in debt and for the cause of Allah and for the [stranded] traveler – an obligation [imposed] by Allah. And Allah is Knowing and Wise.” 
The Meaning of Sadaqah
Lexically, the definition of sadaqah is the truth or sincere gift from a pure heart. While the scholars defined the term as just a gift to get closer to Allah in order to seek the blessings of Allah SWT.
Sadaqah means a gift given to seek rewards from Allah SWT. 
While Ibn Manzur defined sadaqah as what you give for the sake of Allah to the poor and needy. 
Likewise, the same is stated in a hadith in the letter written by Sayyidina Abu Bakar RA:
هَذِهِ فَرِيضَةُ الصَّدَقَةِ الَّتِي فَرَضَ رَسُولُ اللَّهِ صَلَّى اللهُ عَلَيْهِ وَسَلَّمَ عَلَى المُسْلِمِينَ
“These are the orders for compulsory charity (Zakat) which Allah’s Messenger (ﷺ) had made obligatory for every Muslim,” 
The Meaning of Infaq
Infaq according to al-Jurjani means spending your property for those in need. 
In al-Quran, Allah SWT states:
الَّذِينَ يُؤْمِنُونَ بِالْغَيْبِ وَيُقِيمُونَ الصَّلَاةَ وَمِمَّا رَزَقْنَاهُمْ يُنْفِقُونَ
“Who believe in the unseen, establish prayer, and spend out of what We have provided for them,” 
Imam al-Tobari stated the word ‘ينفقون’ in this verse refers to the sanctioning of zakat and providing sustenance for family members and dependants.  Hence, sadaqah and infaq are synonyms.
The Meaning of Wakaf
The terminology wakaf lexically means stop (السكن), prevent (المنع) or withhold (الحبس).  Wakaf lexically also means withholding from trade and others (الْحَبْسُ عَنِ التَّصْرِفِ). The word wakaf, tahbis (تَحْبِيسُ) and tasbil (تَسْبِيل) have the same meaning. This is the meaning understood in most Arab countries, the Wakaf Affairs Ministry is known as (وِزَارًةُ الاَوْقَافِ). Only in Morocco, it is called (وِزَارَةُ الاَحْبَاسِ).
Jurists have agreed on the meaning of the word wakaf lexically with the word “al-Habs” which means withholding for it is similar to the meaning meant in syarak. This is based on the hadith from Saidina Umar RA, Rasullullah PBUH said:
إِنْ شِئْتَ حَبَسْتَ أَصْلَهَا وَتَصَدَّقْتَ بِهَا
“If you wish, you may ‘freeze’ it and give it in charity.” 
Ibn Hajar al-Asqalani explained: “That is giving in the form of wakaf and give its benefits (from the property) in charity.” 
Wakaf in terms of syarak means withholding a certain property for the sake of Allah so that the benefits from it are given to the poor, needy and traveller retaining its original ‘ain (attributes) as the owner of the wakaf given.
The terminology wakaf also means withholding something from being owned and that its benefits are donated. Hence, the ownership changes to Allah SWT’s ownership. 
The hadith narrated from Abu Hurairah RA states that Rasullullah PBUH said:
إِذَا مَاتَ الإِنْسَانُ انْقَطَعَ عَنْهُ عَمَلُهُ إِلاَّ مِنْ ثَلاَثَةٍ إِلاَّ مِنْ صَدَقَةٍ جَارِيَةٍ أَوْ عِلْمٍ يُنْتَفَعُ بِهِ أَوْ وَلَدٍ صَالِحٍ يَدْعُو لَهُ
“When a son of Adam (i.e. any human being) dies his deeds are discontinued, with three exceptions: Sadaqah, whose benefit is continuous; or knowledge from which benefit continues to be reaped, or a righteous child who supplicates for him.” 
Imam al-Nawawi said, the meaning of sadaqah whose benefits are continuous in the above hadith means wakaf. This hadith is also evidence of the validity of wakaf and its tremendous rewards. 
Al-Khatib al-Syarbini said: Scholars have defined the word sadaqah which benefits are continuous in the above hadith to mean wakaf just like what is stated by Imam al-Rafi’i. The reason is the rewards of this sadaqah are continuous while other types of sadaqah aren’t so, its rewards aren’t continuous the same way as sadaqah which its benefits are continuous or wakaf. 
Lastly, we state that the meaning of infaq and sadaqah include the meaning of obligatory zakat, sunnah charity and wakaf. Whilst wakaf has a more specific meaning to the wakaf practice.
May Allah SWT grant us all a true understanding in this religion. Amin.
 Surah al-Taubah: 60. Ibn Abbas R. Anhuma stated that this verse is an explanation about the asnaf group who are entitled to receive zakat. (See al-‘Inayah Syarh al-Hidayah, 2/265) So, it is understood that the word ‘الصَّدَقَاتُ’ here refers to zakat.
Dr. Wahbah al-Zuhaili said: ‘إِنَّمَا الصَّدَقَاتُ’, meaning the obligatory zakat, which is given to the eight groups of asnaf. The letter ‘lam’ in this pronunciation indicates the obligation to give zakat to them, and that, it is specifically for them, it cannot be given to anyone other than them. (See al-Tafsir al-Munir, 5/491)
 See al-Ta`rifat, 1/132
 See Lisan al-Arab, 10/196
 Narrated by al-Bukhari (1454)
 See al-Ta`rifat, 1/39
Surah al-Baqarah: 3
 See Jami’ al-Bayan, 1/244
 See Lisan al-‘Arab, 9/359
 Narrated by al-Bukhari (2772)
 See Fath al-Bari, 5/401
 See al-Ta’rifat, 1/85
 Narrated by Muslim (1631)
 See Syarh al-Nawawi ‘ala Sahih Muslim, 3/89
 See Mughni al-Muhtaj, 10/87