The classic definition of the different types of marriages is given in Manu Smriti.
ब्राह्मो दैवस्तथैवार्षः प्राजापत्यस्तथासुरः । गान्धर्वो राक्षसश्चैव पैशाचश्चाष्टमोऽधमः ॥
“Brāhma, Daiva, Ārṣa, Prājāpatya, Āsura, Gāndharva, Rākṣasa, and Paiśāca which is the worst.”
Brāhma arranged marriage: (Manu 3.27):
आच्छाद्य चार्चयित्वा च श्रुतिशीलवते स्वयम् । आहूय दानं कन्यायाः ब्राह्मो धर्मः प्रकीर्तितः ॥
“When a well-qualified groom of excellent character is invited and the couple is presented with special clothes and worshipped, this is Brāhma marriage.”
Daiva arranged marriage: (Manu 3.28):
यज्ञे तु वितते सम्यगृत्विजे कर्म कुर्वते । अलंकृत्य सुतादानं दैवं धर्मं प्रचक्षते ॥
“When a yajña has been well-performed by the priest, decorating him and giving the bride, is called Daiva marriage.”
Ārṣa arranged marriage: (Manu 3.29):
एकं गोमिथुनं द्वे वा वरादादाय धर्मतः । कन्याप्रदानं विधिवदार्षो धर्मः स उच्यते ॥
“When the bride’s father accepts a gift of one or two bovine couples (i.e. a couple is a cow and a bull) from the groom, and gives his daughter in marriage, this is called Ārṣa marriage.”
Here, commentator Medhātithi says that “dharmatah” means this is strictly for Dharma, and not a business transaction, and there is no intention of buying and selling.
Prājāpatya semi-arranged marriage: (Manu 3.30):
सहोभौ चरतां धर्ममिति वाचानुभाष्य च । कन्याप्रदानमभ्यर्च्य प्राजापत्यो विधिः स्मृतः ॥
“When the couple is given the instruction and benediction saying “May you two tread the path of Dharma together”, and the daughter is given in marriage, and they are blessed, this is Prājāpatya marriage.”
Āsura arranged marriage: (Manu 3.31):
ज्ञातिभ्यो द्रविणं दत्वा कन्यायै चैव शक्तितः । कन्याप्रदानं स्वाच्छन्द्यादासुरो धर्म उच्यते ॥
“When the marriage is done by paying the bride and her relatives as much money as possible, and the wedding itself is done independently, without shāstras, it is called Āsura marriage.”
Gāndharva love marriage: (Manu 3.32):
इच्छयान्योन्यसंयोगः कन्यायाश्च वरस्य च । गान्धर्वः स तु विज्ञेयो मैथुन्यः कामसंभवः ॥
“When the bride and groom have mutual attraction and their union is strictly based on sexual desire, that marriage is called Gāndharva.”
Rākṣasa forced marriage: (Manu 3.33):
हत्वा छित्त्वा च भित्त्वा च क्रोशन्तीं रुदतीं गृहात् । प्रसह्य कन्याहरणं राक्षसो विधिरुच्यते ॥
“When the girl’s family is beaten, their limbs cut off, their homes destroyed, and the girl is forcefully kidnapped, while she is screaming and crying, this type of marriage is called Rākṣasa marriage.”
Paiśāca forced marriage: (Manu 3.34):
सुप्तां मत्तां प्रमत्तां वा रहो यत्रोपगच्छति । स पापिष्ठो विवाहानां पैशाचः प्रथितोऽधमः ॥
“When a woman is taken advantage of, when she is asleep, intoxicated or unconscious, and the man has sex with her without her knowledge, this type of marriage is the worst and most sinful of all marriages, called Paiśāca.”
Here, commentator Medhātithi says that both Rākṣasa and Paiśāca are equally undesirable. In the former there is physical violence, in the latter there is deception.
The commentary of Medhātithi and others provide so much valuable detailed information and context.
All the types of unions or marriages seen in the world are described above. Every situation in history and in the modern world is also covered.
An important point to note is that none of the marriages described involve the bride’s family giving any kind of dowry to the groom’s family. If anything, the opposite is seen, where the groom gives gifts to the bride's family.