An envelope is what we all think - something that contains a letter.
A "flat" means essentially that - it is flat. As compared to a package.
But also normally larger than a standard envelope in length and width (think "manilla" envelope).
Don't confuse "Flat" with "Flat Rate".
One refers to the packaging (flat), the other (Flat Rate) to the cost of shipping (and it requires pre-labeled packaging available from USPS).
: "Soft-pack envelopes are usually cloth, plastic, or vinyl packaging that is flexible enough to adhere closely to the contents being packaged and strong enough to securely contain the contents. This packaging has a measurable shape before being used but can conform to the shape of its content and will permit any excess air to escape to ensure that it takes up minimum cubic space while protecting the contents. Cubic measurement is done prior to items being placed in the envelope." (USPS web site)
So what that means for everyday use - "soft pack" is an envelope (usually larger, but not always) that is padded or very flexible in some manner (bubble, Tyvek, fiber). The contents make the package no longer flat like a letter, but the physical size of the package still resembles a flat (or large envelope).
Using this size will return various rates - including commercial cubic pricing not available at the local post office.