Bends ~ as nouns ~ are gentle curves inflicted on flexible material like paper. They suggest a turning through a small angle.
When used as a verb to bend can be an instruction to do rather more as in "bend the paper round the corner, or broomstick". It can have a broad meaning covering all those below.
Folds are sharper ~ more pronounced ~ than bends. On an increasing scale they fall into divisions such as ~
A soft fold is one where the paper springs back of its own accord and is not distorted in any way: so that it returns to its normal flattened state of its own accord. Large sheets of paper are sometimes bundled into a soft fold to fit into a box. Sheets of A3 paper can be soft folded to hug the base, side, and top of a box which is small enough to classify as a Royal Mail Small Parcel [125515]]. Fabric is usually softly folded for storage. A bolt of cloth is a form of continuous or multi-soft folds.
Soft folds are a good way of protecting papers when they are in transit. (Beware: even a single sheet sent through the post as a roll can be larger than any parcel, and can be quite costly. Some carriers are less sensitive to length.)
I use loosely folded as a term in between soft and hard. A sharp enough fold to enable reduction of bulkiness in folios (for storage or transit) but a fold that is possibly slightly inaccurate as regards bisection. Accurate re-alignment of the geometry of the fold enables the fold to be amended to an accurately placed crease. When we sell folios in our shop we try to keep the folds loose enough to enable recipients to improve on them if required. We cannot aim to provide creases to the level of accuracy that some customers may (rightly) expect, and so leave the final pressing to them.
If making folios the easy way [123803], by bending a whole section at a time, the inner folios of the section may be hard creased, the outer ones less so. If the outer ones are removed from the section they will probably need to be creased separately, especially if the width of the book is to be kept low.
A hard fold is one where the fold permanently marks ~ crumples ~ squashes ~ damages the paper such that its bending properties are altered.
A crease is a hard fold which has been pressed down with sufficient pressure to emphasise the hardness of the fold to maximum intensity.
Those practising origami, bookbinding and bookcrafts develop their own techniques for obtaining "good"folds. I am happy to share my advice [123858]. Readers are welcome to contribute.
The important thing is to avoid a crease when or where it is not wanted, and to use one where it helps achieve some a desired aim.