The notion of 'feudalism' as a common medieval political and social structure is pretty contentious, and a better informed user like /u/idjet could probably describe it way better than I could. I'll write about the origins of the clan system and its military, economic and social purposes.

The "clan" originated in Ireland as the most basic social and economic unit in early Gaelic society. It was an extended family group that often coincided with a tuath, the most basic territorial and political unit, which contained a variation of land (bogs for peat, woods for swine raising, meadows for cattle and horses, arable land for crops) held in common that made the clan economically self-sufficient. Sometimes, a clan might have trans-regional links over two or more tuatha. An average tuath has been estimated to have been around 16km in diameter, with an average of around 3000 inhabitants living in nucleated farmsteads.

The actual purpose of a clan was to serve as a "low-energy war-machine"; because it was ideally self-sufficient, it could use its surplus resources to support a warrior-elite drawn from its own members. These warriors would be engaged in sporadic and almost-constant low-intensity warfare, raiding neighboring polities for cattle (the basic unit of currency) or defending their own, or else they were called upon by regional overlords of several tuatha to take part in dynastic feuds. There would be one ri tuatha (I suppose you could call them a chieftain, they were the aristocratic leaders of a tuath) who maintained a retinue of lesser warrior-aristocrats through a system of cattle-renting clientship. The same system of cattle-renting made farmers provide the aristocracy with food-surplus and labour. These chieftains were often subordinate to a regional king who rented them cattle (which he rented to his subordinates), several of whom might be subordinate to a major provincial king. Interestingly, there was no law that forced an individual to be a client of a single king; he could rent from up to three nobles which created a complicated system of overlapping hierarchies.

The clan supported the warrior-aristocracy through seasonal-feasts which used up all of their surplus food products. These feasts are described in a lot of early literature, and legal texts like the Lebor na Cert tell us that when not at war, an aristocrat and his retinue would travel across his territory, constantly being fed and hosted by his subordinates.

Archaeologists like Nerys T. Patterson suggest that the clan model (ie., an extended and economically self-sufficient family group which supported a small caste of warrior-aristocrats) was a common form of social organization in Pre-Roman temperate Europe, especially in Gaul.

If I had to summarize an answer to your question, it would be: feudalism is generally defined as a system of military obligations and hierarchies in post-Roman western Europe, while the clan system was the most basic unit of another, unrelated system of military hierarchy and obligations that derived from Iron-Age social structures.