The former, the package tour Algarve, stretches along the south coast from the Spanish border in the east, to Praia de Luz in the west, with tourism most heavily concentrated in the area between Faro, Albufeira and Portimao. The "rest" includes the southwest tip of Portugal, the West coast of the Algarve, and the hinterland.
In a Which? (UK consumer magazine) survey of major European seaside resorts in 2023, the three main resorts of the Algarve all finished in the bottom ten (out of 44) for general ranking and for attractiveness. By contrast, up-market Tavira, away from the main resorts, was in the top ten.
In its favour, as coastal areas go, the south-facing Algarve coast has a lot of long sandy beaches, like Mediterranean beaches with tides. Low lying in the east, the coast becomes rockier towards the west, but with plenty of beaches. West of Lagos, the coastline is wilder and less built up, towns are on a smaller scale, and there is hardly a high-rise building to be seen.
Away friom the popular beaches and resorts on the south coast, the west coast of the Algarve, stretching north from Cape St. Vincent, offers some wild and rugged coastline with sandy coves, black cliffs and wonderful views. The rugged west coast is the southern part of Alentejo and Vicentine Coast Natural Park, which includes much of Portugal's west-facing Atlantic coast and is much less developed, but with equally stunning views and black cliffs.
Inland from the south coast, the Algarve region is rural, with a mix of farmland hills and forest. For hikers, the Via Algarviana, the Portuguese GR 13 hiking trail, crosses the region from east to west (or the reverse, as you wish) from Alcoutim on the river Guadiana, on the Spanish border to Cape St. Vincent in the southwest.
The Algarve can be easily reached by air, and the regional airport at Faro is well connected with the rest of Europe (See How to get to Portugal). The region is easily reached by train from Lisbon, and a rail line runs all along the coast from Vila Real de Santo Antonio at the mouth of the Guadiana river, as far as Lagos in the west, and connects all the main resorts.
The other side of the Algarve - Hiking on the Via Algarviana
Map from OpenStreetMap