Seem, look, appear can mean to be as stated in one’s view or judgment, but not necessarily in fact.
Often they are used interchangeably with apparently no difference in meaning.
But even in such phrases seem suggests an opinion based on subjective impressions and personal reaction rather than on objective signs while look implies that the opinion is based on a general visual impression.
Appear may convey the same implication as look but it sometimes suggests a distorted impression such as can be produced by an optical illusion, a restricted point of view, or another’s dissembling.