Householder, opposite of Agāra (homeless) or anagāriyā, independend whether having gone for refuge or not. An householder, having taken refuge will be usually called Upāsaka (masc.) or Upāsika (fem.). Spiritual wanderer are called pabbajita and usually refers to those haven left home under the Tripple Gems.
by late Ven. Nyanatiloka Thera:
by the Pali Text Society:
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by Ven. Thanissaro Maha Thera:
Suttas and Dhammadesanā