The prefixes นัก- and นาย- in Thai professions reflect a mix of linguistic, historical, and cultural influences, as well as the nature of the professions themselves. Here’s a breakdown of their etymology, history, and usage:

1. นัก- Prefix
Etymology: The prefix "นัก-" comes from Pali and Sanskrit influences, common in Thai due to the historical impact of Indian culture, Buddhism, and Brahminism on the language. It originally carried a sense of "one who is skilled in" or "a person engaged in" a specific activity or field.
Usage: "นัก-" is typically used for professions or roles that involve skill, knowledge, study, or active engagement, often with an intellectual, creative, or specialized connotation.
Type of Profession: Commonly attached to roles associated with learning, expertise, or performance. Examples include:
นักเรียน (nák-rîian) – student ("one who studies")
นักเขียน (nák-khǐian) – writer ("one who writes")
นักวิทยาศาสตร์ (nák-wít-thá-yá-sàat) – scientist ("one engaged in science")
นักดนตรี (nák-don-dtree) – musician ("one who performs music")

Historical Context: This prefix gained prominence as Thai society modernized, especially during the 19th and 20th centuries, when new fields of study and professions emerged due to Western influence, education reforms, and globalization. It’s often used for "modern" or skill-based roles.

2. นาย- Prefix
Etymology: "นาย-" derives from the Thai word นาย (nâai), meaning "master," "lord," or "chief." It has roots in feudal and hierarchical structures, reflecting authority, leadership, or ownership. It’s a native Thai term, tied to social organization in traditional Thai society.
Usage: "นาย-" denotes a position of authority, leadership, or responsibility, often in practical, administrative, or hands-on roles.

Type of Profession: Typically applies to roles involving oversight, command, or manual leadership. Examples include:
นายช่าง (nâai-châang) – craftsman or technician ("master of craft")
นายทหาร (nâai-thá-hǎan) – soldier or officer ("master of the military")
นายก (nâai-gòk) – leader, e.g., นายกรัฐมนตรี (prime minister, "master of state ministers")

Historical Context: This prefix reflects Thailand’s feudal past, where "นาย" was used for landlords, bosses, or those in charge of labor or resources, as in the sakdina system (a hierarchical land-based social structure). It carried over to certain trades and official roles as society evolved.

3. Key Differences
Nature of Work:
นัก-: Emphasizes skill, expertise, or intellectual pursuit; often tied to modern, specialized, or creative fields.
นาย-: Implies authority, leadership, or practical responsibility; often linked to traditional, hierarchical, or hands-on roles.
Historical Development:
นัก- is more tied to Pali/Sanskrit and the influx of new professions during modernization (19th–20th centuries, especially under King Rama V’s reforms).
นาย- is rooted in native Thai social structures, predating modern influences, and reflects power dynamics from feudal times.
Cultural Perception:
นัก- feels dynamic and active, suggesting ongoing engagement or mastery through skill.
นาย- conveys respect, status, or control, often tied to a position of dominance or experience.
4. Professions Without These Prefixes
Your assumption is partly correct! Professions lacking นัก- or นาย- often have older, standalone terms or borrowed words that predate or bypass these conventions:

Older Native Terms: Words like ชาวนา (châao-nâa, farmer) come from "chao" (person/people) and "na" (field), reflecting ancient agricultural roots in Thai society, long before prefixes like นัก- or นาย- became systematic.
Borrowed Words: Modern professions often adopt foreign terms, especially from English, without prefixes, e.g.:
วิศวกร (wít-sà-wá-gôn) – engineer, from Sanskrit "visvakarma" (master of works), adapted via Western contact.
แพทย์ (phâet) – doctor, from Sanskrit "vaidya" (healer), entrenched in Thai before modern prefix trends.
Reason: These terms either emerged early in Thai history, tied to basic societal roles (farming, healing), or were imported during modernization without needing a prefix to clarify their nature.
5. Is There a Reason or Pattern?
Yes, but not rigid: The choice of prefix (or lack thereof) isn’t random but isn’t strictly codified either. It’s shaped by:
Linguistic Tradition: Pali/Sanskrit for นัก-, native Thai for นาย-.
Historical Timing: Older roles (farmer, doctor) often stand alone; newer ones (scientist, programmer) take นัก-; leadership roles (craftsman, officer) take นาย-.
Type of Work: Intellectual/creative = นัก-; authoritative/practical = นาย-.
Flexibility: Some professions can shift or lack consistency, e.g., cultural or regional naming habits might influence usage.
Conclusion
The นัก- prefix highlights skill and specialization, rooted in Pali/Sanskrit and modern influences, while นาย- reflects authority and tradition, tied to Thai feudal roots. Professions without either often have ancient origins or borrowed forms that didn’t require prefixes. This pattern evolved from a blend of linguistic heritage, social hierarchy, and the demands of a modernizing Thailand, especially from the 19th century onward.