in what ways does An chi(lin kuei art) is different than Yin sen shu (beggar art)?

Lin Kuei or Lín Guǐ in Chinese literally "Forest Demons." "Tengu" is another type of Forest demon which lives in the mountains and taught martial arts to selected Samurai. I don't know if the Lin Kuei had ever taught any martial arts. Maybe there could been some link between Tengu and Lin Kuei but lost through time.

"Beggars style" also called "wanderer's or vagabond's style" is a Chinese martial art which concentrates on the most deadliest techniques from an assortment of kung fu systems. Japanese Ninjutsu was said to have it's foundations from the Beggars style. The Beggars style is a rare martial arts system, fortunately there is a branch of Pak Mei kung fu which has preserved a good portion of the Wanderer's style.

Is this another question about some movie or cartoon martial arts? If the styles you mention are real they would be so rare than no one here is likely to know anything about them. If they are movie or cartoon based they are no relevant here.