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An hour and twenty minutes after being inserted into low Earth orbit at 17,175 mph (27,640 km/h), the SLS Interim Cryogenic Propulsion Stage (ICPS) performed the Trans-Lunar Injection (TLI) burn which accelerated the Orion spacecraft towards the Moon at a velocity of about 22,600 mph (36,371 km/h).

According to Apollo by the Numbers the velocity after the TLI burn performed by the S-IVB stage ranged from 24,129 mph (38,832 km/h) for Apollo 12, to 24,258 mph (39,039 km/h) for Apollo 15.

The Apollo and Artemis I missions used different trajectories to reach the Moon. The Saturn V TLI burns placed the spacecraft on a less efficient free-return trajectory that would have looped around the Moon and returned to Earth if a Lunar Orbit Insertion (LOI) burn was not performed by the Apollo spacecraft. This provided a safety margin in case a problem occurred during the trip to the Moon (as actually happened on Apollo 13).

Artemis I was a non-crewed mission which used a very different trajectory than will be used on the crewed Artemis missions. The Artemis I TLI trajectory was not free-return. Approaching the Moon the Orion spacecraft performed two primary burns, the Outbound Powered Flyby (OPF) and Distant Retrograde Insertion (DRI), which placed Orion into a Distant Retrograde Orbit.

Artemis II will be a crewed non-landing, non-orbiting mission and will use a free-return trajectory.

Artemis III will place Orion into a Near-Rectilinear Halo Orbit (NRHO) where the the crew will transfer to a lunar lander. Starship HLS is the currently planned lander.

An hour and twenty minutes after being inserted into low Earth orbit at 17,175 mph (27,640 km/h), the Artemis I SLS Interim Cryogenic Propulsion Stage (ICPS) performed the Trans-Lunar Injection (TLI) burn which accelerated the Orion spacecraft towards the Moon at a velocity of about 22,600 mph (36,371 km/h).

According to Apollo by the Numbers the velocity after the TLI burn performed by the Saturn S-IVB stage ranged from 24,129 mph (38,832 km/h) for Apollo 12, to 24,258 mph (39,039 km/h) for Apollo 15.

The Apollo and Artemis I missions used different trajectories to reach the Moon. The Saturn V TLI burns placed the Apollo spacecraft on a less efficient three-day trajectory, which was also a free-return trajectory that would have looped around the Moon and returned to Earth if a Lunar Orbit Insertion (LOI) burn was not performed by the Apollo spacecraft. This provided a safety margin in case a problem occurred during the trip to the Moon (as actually happened on Apollo 13).

Artemis I was a non-crewed mission which used a very different trajectory than was used on the Apollo lunar missions, as well as being different from what will be used on the crewed Artemis II and Artemis III flights. Artemis I used a more efficient five-day trajectory to reach the Moon, and was not free-return. Two post TLI burns performed by the Orion spacecraft (not counting course corrections) placed Orion into a Distant Retrograde Orbit.

Artemis II will be a crewed non-landing, non-orbiting mission and will use a free-return trajectory. However like Artemis I it will take more than three days for Artemis II to reach the Moon using a more efficient trajectory than Apollo. After separating from the ICPS the Orion spacecraft will make several burns on the way to the Moon as part of a Multi-Trans-Lunar Injection (MTLI) method.

For Artemis III Orion will be placed into a Near-Rectilinear Halo Orbit (NRHO) where the the crew will transfer to the Starship HLS lunar lander.

The Artemis I velocity was about 22,600 mph (36,371 km/h) at the conclusion of the trans-lunar injection (TLI) burn performed by the Interim Cryogenic Propulsion Stage (ICPS). According to Apollo by the Numbers the Saturn V velocity after the TLI burn performed by the S-IVB stage ranged from 24,129 mph (38,832 km/h) for Apollo 12, to 24,258 mph (39,039 km/h) for Apollo 15.

The Apollo and Artemis missions used different trajectories to reach the Moon. The Saturn V TLI burns placed the spacecraft on a less efficient free-return trajectory that would have looped around the Moon and returned to Earth if a Lunar Orbit Insertion (LOI) burn was not performed by the Apollo spacecraft. This provided a safety margin in case a problem occurred during the trip to the Moon (as actually happened on Apollo 13).

The Artemis I 22,600 mph TLI number is based on the following sources:

NASA pre-launch document 24,500 mph
NASA TV live broadcast commentary (5:00:22) November 16, 2022 - 22,500 mph
CNN Interactive November 16, 2022 - 22,600
CollectSpace November 16, 2022 - 22,670

Apollo TLI

An hour and twenty minutes after being inserted into low Earth orbit at 17,175 mph (27,640 km/h), the SLS Interim Cryogenic Propulsion Stage (ICPS) performed the Trans-Lunar Injection (TLI) burn which accelerated the Orion spacecraft towards the Moon at a velocity of about 22,600 mph (36,371 km/h). 

According to Apollo by the Numbers the velocity after the TLI burn performed by the S-IVB stage ranged from 24,129 mph (38,832 km/h) for Apollo 12, to 24,258 mph (39,039 km/h) for Apollo 15.

The Apollo and Artemis I missions used different trajectories to reach the Moon. The Saturn V TLI burns placed the spacecraft on a less efficient free-return trajectory that would have looped around the Moon and returned to Earth if a Lunar Orbit Insertion (LOI) burn was not performed by the Apollo spacecraft. This provided a safety margin in case a problem occurred during the trip to the Moon (as actually happened on Apollo 13).

The Artemis I 17,175 mph LEO number is from the NASA TV live broadcast commentary (timestamp 3:36:16) on November 16, 2022

The Artemis I 22,600 mph TLI number is based on the following sources:

NASA pre-launch document - 24,500 mph
NASA TV live broadcast commentary (timestamp 5:00:22) November 16, 2022 - 22,500 mph
CNN Interactive November 16, 2022 - 22,600
CollectSpace November 16, 2022 - 22,670

Apollo TLI (from Apollo by the Numbers)

The Apollo and Artemis missions used different trajectories to reach the Moon. The Saturn V TLI burns placed the spacecraft on a less efficient free-return trajectory that would have looped around the Moon and returned to Earth if a Lunar (Orbit Insertion (LOI) burn was not performed by the Apollo spacecraft. This provided a safety margin in case a problem occurred during the trip to the Moon (as actually happened on Apollo 13).

Additional Info:

The Apollo and Artemis missions used different trajectories to reach the Moon. The Saturn V TLI burns placed the spacecraft on a less efficient free-return trajectory that would have looped around the Moon and returned to Earth if a Lunar Orbit Insertion (LOI) burn was not performed by the Apollo spacecraft. This provided a safety margin in case a problem occurred during the trip to the Moon (as actually happened on Apollo 13).

Additional Info: