Full Idea
∈ relates across layers (Plato is a member of his unit set and the set of people), while ⊆ relates within layers (the singleton of Plato is a subset of the set of people). This distinction only became clear in the 19th century.
Gist of Idea
∈ relates across layers, while ⊆ relates within layers
Source
William D. Hart (The Evolution of Logic [2010], 1)
Book Reference
Hart,W.D.: 'The Evolution of Logic' [CUP 2010], p.5
A Reaction
Getting these two clear may be the most important distinction needed to understand how set theory works.
Related Ideas
Idea 13201 ∈ says the whole set is in the other; ⊆ says the members of the subset are in the other [Enderton]
Idea 12337 There is 'transivity' iff membership ∈ also means inclusion ⊆ [Badiou]
Idea 15500 Classes divide into subclasses in many ways, but into members in only one way [Lewis]
Idea 15499 A subclass of a subclass is itself a subclass; a member of a member is not in general a member [Lewis]