Does infect deal damage to players as poison counters and to creatures as -1/-1 counters at the same time?

Infect is a keyword ability defined in CR 702.90. It changes the way damage dealt by the permanent (or spell) is applied: damage to players is dealt as poison counters instead of loss of life, and damage to creatures is dealt as -1/-1 counters instead of regular damage marked on the creature. Both conversions happen as a result of the same keyword — they are two sides of one rule, not two separate abilities.

CR 702.90a states: 'Infect is a static ability. Damage dealt to a player by a source with infect doesn't cause that player to lose life. Rather, it causes that player to get that many poison counters. Damage dealt to a creature by a source with infect doesn't use the damage system. Rather, it causes that many -1/-1 counters to be placed on that creature.'

The two effects apply simultaneously because they are both simply describing how damage from that source is processed. There is no timing difference between them — they are both consequences of the same damage event being resolved under infect's rules modification.

Concrete example: Your opponent controls a 3/3 creature and has 0 poison counters. You attack with a 3/3 creature with infect and your opponent blocks. Both players choose to deal their damage simultaneously in combat (CR 509.2). The opposing 3/3 receives three -1/-1 counters (making it 0/0, causing it to die to state-based actions), while your infect creature's 0 damage to the player is irrelevant here. If the attack were unblocked instead, the player would receive 3 poison counters rather than losing 3 life — no life loss occurs at all.

Note: a source with infect always uses both conversions wherever applicable. You cannot apply only one of the two effects; they come as a package under the single keyword.