What's the difference between them? I couldn't properly come up with any examples or contexts with them respectively.
From the website lexology.com, 4/20/19:
 After success against Comcast with an earlier action at the ITC [the International Trade Centre], TiVo is once more seeking an exclusion order as it looks to hurt its rival’s cable platform.
Looks with with complement the active infinitive to hurt, and the infinitive taking the object platform. The meaning is "seeks to harm."
From the website www.barrons.com, 9/5/19:
 The uncertainty looks to be hurting GE's share price.
Looks with complement the infinitive to be, and the infinitive taking as a complement the active progressive infinitive to be hurting. The meaning is "appears as inducing ongoing harm."
Note that there is a another, somewhat informal usage, as illustrated at the website www.nunesmagician.com, 3/2/18:
 Since that game, he looks to be hurting and the numbers would indicate that something isn't right.
Looks with the infinitive to be, and the infinitive taking as a complement the adjectival present participle "hurting." The meaning is "appears as suffering."