Swimming is treated separately from showering, and the advice is stricter.
The same instruction shows up after different surgeries. After a cesarean section: do not soak in a bathtub or hot tub, or go swimming, until your provider tells you it is OK. After open gallbladder surgery: do not soak in a bathtub, hot tub, or go swimming until your provider tells you it is OK.
For a cesarean section, there is a timeframe: in most cases, this is not until three weeks after surgery. That figure belongs to that operation. It is not a general rule for wounds. It’s included here to show how long the wait can be, not to be applied to your wound.
The reason comes from general care of surgical wounds, where showers are preferred to baths: in a shower, the wound does not soak in the water, and soaking the wound could cause it to reopen or become infected. Swimming means putting the wound under water, and that is the thing being avoided.
For wounds that are not surgical, the answer is shorter. It will differ depending on the type of wound, so you need to discuss it with your healthcare professional. Waterproof dressings are available.
This page doesn’t treat a pool, the sea, a lake or a hot tub any differently. The one instruction that covers them all: wait until the person treating the wound says it is all right.