The Lord’s first expansion is Lord Balarama. Lord Balarama expands into the first Catur-vyuha. The Catur-vyuha, Their expansions and the vilasa (pastime) incarnations of the Lord fall under the tad-ekatma category of forms of the Lord. Tad-ekatma forms resemble the svayam-rupa form, with differences.
The Catur-vyuha are categorized as svamsa (sva means ‘own’; and amsa means ‘part’) or expansions of the Lord. The Lord’s prabhava expansions divide into vibhava expansions: Vasudeva, Sankarsan, Pradyumna and Aniruddha. This first Catur-vyuha expands into the 24 vaibhava-vilasa forms of Vishnu, which preside over the Vaikuntha planets [CC M 20.191]. Catur means ‘four’, and vyuha means ‘guard’ or ‘arms’. The word Catur-vyuha means the incarnations of the Lord who have four arms and guard the four directions.
Lord Narayana expands from Sankarsana. The second Catur-vyuha – Vasudeva, Sankarsana, Pradyumna and Aniruddha – expands from Narayana. The purusa-avataras expand from the Sankarsana of the second Catur-vyuha. There are thus two divisions of avataras in the svamsa category: those coming from Sankarsana ie. the purusa-avataras; and the lila-avataras.