See you next week. See you next week. What's the difference between the two sentences?

Your question can be summed up as a comparison between the future continuous tense and the ordinary future tense:

Their meanings are basically the same, but they are slightly different in the following two aspects.

Difference one, different tone

The future continuous tense is more euphemistic and polite in tone than the ordinary future tense.

See you next week. See you next week. (The tone is direct, which may be what the boss said to his subordinates and what the elder said to the younger generation)

See you next week. I will meet you next week. (Euphemistic tone may be the expression of subordinates to superiors and younger generations to elders)

Second, the emphasis is different. Generally speaking, the future tense focuses on subjective will, while the future continuous tense emphasizes action.

See you next week. See you next week. (emphasizing subjective commitment and willingness)

See you next week. I will meet you next week. (emphasize that the plan will happen at some time in the future, and emphasize that this time is in progress)

I hope it helps you!