Short answer
HubSpot's developer docs: segments have three processingType values. DYNAMIC segments are filter-based and HubSpot adds and removes records as they change. MANUAL segments only change by user or API. SNAPSHOT segments process filters once, then only change manually. New segments return an ILS listId.
1. In the app
Segment types in my demo portal.

2. The calls
GET /crm/v3/lists/{listId}/memberships
PUT /crm/v3/lists/{listId}/memberships/add body: ["123", "456"]
PUT /crm/v3/lists/{listId}/memberships/add-from/{sourceListId}Paths shown in v3 form; the docs list dated API versions too.