Astrazeneca uses a modified chimpanzee adenovirus vector. Sputnik uses a modified hybrid human adenovirus vector. Since many (most?) humans have been previously exposed to human adenoviruses (but not chimp adenoviruses), some will have previously-existing antibodies and cellular immunity that may be enough to block a human-adenovirus-based vaccine from fully working. This is also a likely problem with at least one of the Chinese adenovirus-based vaccines.
None of the vaccines "require" one dose or two doses (or even three :) -- it's just a choice made by the manufacturer, trading off convenience vs. level of protection. Since clinical trials are complex and time-consuming, each had to choose an initial dosing regime. The more doses, the better the expected level of protection, but the more complicated the administration (records of when billions of people got their first shots and are due for second ones!), and the more doses needed.
The difference in efficacy is likely mostly because they are different vaccines, but is also affected by the number of doses and the amount of viral vector used for one dose. Astrazeneca made some dosing mistakes in their trial and surprisingly found that the smaller of the two amounts of vector they were testing worked better!
"COVID-19: How do viral vector vaccines work?"
"A Novel Chimpanzee Adenovirus Vector with Low Human Seroprevalence: Improved Systems for Vector Derivation and Comparative Immunogenicity"
"Sputnik V COVID-19 vaccine candidate appears safe and effective"