Assuming that you are comparing modern bailout parachute and skydiving reserve parachutes there are many differences of note. I have more knowledge of the latter and so my bias is in this favour.
A bailout/emergency pilot is rarely expected to be used and therefore a pilot is unlikely to have undertaken detailed practical training on its use. It is not uncommon as a passenger required to wear such a parachute, to be told how to exit the air craft and then deploy it only, with limited practical rehearsal. By contrast Skydivers perform many rehearsals as part of their training. Furthermore, modern day skydiving reserve parachutes, are similar to the design of the main parachute, so by virtue of being trained to ‘pilot’ the main, the skydiver will have considerable knowledge to apply to the piloting of the reserve, even if reserve use occurs on their first jump.
Square parachutes typically take longer to deploy than round ones. Additionally the round parachute opening characteristics are more consistent. These factors, make round parachutes more appropriate for ultra low level use as might be required in an emergency last resort scenario faced by a pilot. Conversely, most skydivers should face their problems at a higher deployment altitude >2500ft typically, where the opening characteristics are less pronounced. Don’t get me wrong - square parachutes can be opened at exceptionally low altitudes too, for example base jumping but the use case, equipment and prep are somewhat different.
Skydivers use square parachutes for a multitude of reasons, but a key factor is manoeuvrability. It makes sense that a reserve parachute should be of similar performance to allow the user to land at a safest possible place of their choosing. Being able to steer provides an additional element of opportunity to avoid some obstacles assuming appropriate training, experience and presence of mind.
A modern skydiving reserve parachute is typically integrated into the same external container used for the main parachute for that sole purpose. Many bailout parachutes are integrated into harness systems which serve other purposes, inc restraint, comfort, buoyancy etc.
Aside from the obvious physical differences between the round and square parachute, there will be other features that differ a reserve parachute from a main one. Canopy shape will often differ to ensure a more consistent opening and docile handling characteristics, vs sportier main parachutes. Profile and number of cells are common changes.
A skydiving reserve is designed to be deployed independently of a main parachute, but to be compatible should an inadvertent or deliberate deployment of both occur. The reserve parachute will typically have shorter lines to allow (and encourage) both canopies to fly side by side if needed. There are other differences in how both are packed and deployed, again to enhance the opportunity for the reserve to deploy effectively, but there are many customisations based on risks associated with particular types of jump, that make this difficult to summarise.
Finally a reserve parachute does not have a user operated release method such as a capewell, as it is integrated into the load bearing structure of the skydiving container and the harness would need to be removed. By contrast some bailout parachutes allow disconnection to allow for uncontrollable hazardous landings such as into water, or in high wind situations where being dragged on the ground is more possible. E.g landing on roof of building.
Finally to answer your points more specifically.
Given the difference between the two types of parachute, there has been significant divergence between manufacturers, although (if memory serves there are some manufacturers who do both) but typically there is more in common with military parachuting and emergency parachute manufacturers.
There are some material physical differences, but these are less important than the characteristics above.