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Coma and field curvature are different aberrations. Coma distorts objects towards the edge of the field of view making stars look like comets with tails pointing away from the centre of the FOV. Field curvature results in a difference in focus between the centre and edges of the FOV. You can have things in focus at the centre or at the edges but not both at the same time.
Coma is the main aberration affecting Newtonian reflectors, so you'll generally need a coma corrector for AP using one unless you have a small sensor or a slow scope (f/ratio like f/8 or greater.)
Field curvature is an issue with other designs such as refractors. That's why field flatteners are available for these scopes. Some refractors designed specifically for AP, the Takahashi FSQ scopes for example, have extra lens elements to produce a flat field without further correction.
Cheers,
Rick.
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