Question: Are the Garajonay National Park and Caldera de Taburiente National Park located on the same island?

Context articles: Idafe Rock
Hermigua
Roque de los Muchachos
Echium wildpretii subsp. trichosiphon
Caldera de Taburiente National Park
Garajonay National Park
Crater Lake National Park
Echium gentianoides
Valles Caldera
Barlovento, Santa Cruz de Tenerife

Idafe Rock is a natural stone pillar located in Caldera de Taburiente National Park on the island of La Palma in the Canary Islands.
Hermigua is a town and a municipality in the northeastern part of La Gomera in the province of Santa Cruz de Tenerife of the Canary Islands, Spain.
 It is located 12 km northwest of the island's capital, San Sebastián de la Gomera.
 The Garajonay National Park covers the southern part of the municipality.
Roque de los Muchachos (English: "Rock of the Boys") is a rocky mound at the highest point on the island of La Palma in the Canary Islands, Spain.
 The rocks are found at an elevation of 2,423 m above sea level, not far from the Observatorio del Roque de los Muchachos, where some of the world's largest telescopes are situated; the altitude and the dryness of the climate here give rise to excellent observing conditions.
 The rocks are contained with the Parque Nacional de la Caldera de Taburiente.
Echium wildpretii" subsp.
 "trichosiphon is an "Echium" that is found high up in the area of La Caldera de Taburiente on the Canary Island of La Palma.
 Like its sister plant on Tenerife, this plant forms a large rosette of silvery leaves which eventually give rise to tall spikes of bright pink flowers.
 The plant is biennial and dies after flowering.
 This plant can be grown in gardens, but requires good drainage and fairly mild conditions.
 The plant hates water falling in the centre of the rosette and will often rot in such conditions.
Caldera de Taburiente National Park (Spanish: "Parque Nacional de la Caldera de Taburiente" ) is large geological feature on the island of La Palma, Canary Islands, Spain.
 It contains the enormous expanse of the Caldera de Taburiente which dominates the northern part of the island, and was designated as a national park in 1954.
 The telescopes of the Roque de los Muchachos Observatory are situated very close to the summit.
Garajonay National Park (Spanish: "Parque nacional de Garajonay" , ] ) is located in the center and north of the island of La Gomera, one of the Canary Islands (Spain).
 It was declared a national park in 1981 and a World Heritage Site by UNESCO in 1986.
 It occupies 40 km (15 sq mi) and it extends into each of the six municipalities on the island.
Crater Lake National Park is a United States National Park located in southern Oregon.
 Established in 1902, Crater Lake National Park is the fifth-oldest national park in the U.S. and the only national park in Oregon.
 The park encompasses the caldera of Crater Lake, a remnant of a destroyed volcano, Mount Mazama, and the surrounding hills and forests.
Echium gentianoides is a synonym of "Echium thyrsiflorum" , a flowering plant in the borage family Boraginaceae with brilliant blue tubular flowers.
 It is endemic to the island of La Palma, the Canary Islands.
 It occurs in one location of La Caldera de Taburiente where it grows in sunny, rocky sites at altitudes higher than 1.800 m.
 The main threat described for this species is predation by goats.
Valles Caldera (or Jemez Caldera) is a 13.7 mi wide volcanic caldera in the Jemez Mountains of northern New Mexico.
 Hot springs, streams, fumaroles, natural gas seeps and volcanic domes dot the caldera floor landscape.
 The highest point in the caldera is Redondo Peak, an 11253 ft resurgent lava dome located entirely within the caldera.
 Also within the caldera are several grass valleys ["Valle(s)"] the largest of which is Valle Grande ( ), the only one accessible by a paved road.
 Much of the caldera is within the Valles Caldera National Preserve, a unit of the National Park System.
Barlovento (Spanish for windward) is a municipality in the northern part of the island of La Palma, one of the Canary Islands, and a part of the province of Santa Cruz de Tenerife.
 Barlovento is on the main highway which encircles the island.
 The land rises steeply from a small coastal plain, to the rim of the Caldera de Taburiente at Pico de la Cruz (2,350m)