They are generally called Regierungsrat (Executive Council) in German-speaking cantons and Conseil d'État (State Council) in French-speaking cantons.
The above mentioned collegial bodies are formally chaired by a president.
The elected member who has also received the most votes for president takes that office for the entirety of their term on the council, i.e. 4 years.
For example, the elections in Aargau were held in 2020, but the tenure of the new Executive started on 1 January 2021.
Parties Note: due to the multiple official languages of Switzerland, parties may have more than one abbreviation List as of July 2, 2022: (president first and in bold) Markus Dieth (CVP) Dexter Egli (SP) Alex Hürzeler (SVP) Jean-Pierre Gallati (SVP) Yves Noël Balmer (SP) Hansueli Reutegger (SVP) Paul Signer (FDP) Alfred Stricker (Ind) Monika Rüegg Bless (Centre) Ruedi Eberle (SVP) Roland Inauen (Ind) Stefan Müller (Ind) Ruedi Ulmann (centre) Jakob Signer (Ind) Anton Lauber (Centre) Isaac Reber (Green) Kathrin Schweizer (SP) Thomas Weber (SVP) Conradin Cramer (LDP) Lukas Engelberger (Centre) Stephanie Eymann (LDP) Esther Keller (GLP) Tanja Soland (SP) Kaspar Sutter (SP) Evi Allemann (SP) Astrid Bärtschi (Centre) Christoph Ammann (SP) Philippe Müller (FDP) Christoph Neuhaus (SVP) Pierre Alain Schnegg (SVP) Sylvie Bonvin-Sansonnens (Green) Didier Castella (FDP) Romain Collaud (FDP) Philippe Demierre (SVP) Jean-Pierre Siggen (Centre) Jean-François Steiert (SP) Antonio Hodgers (Green) Thierry Apothéloz (SP) Serge Dal Busco (Center) Anne Emery-Torracinta (SP) Fabienne Fischer (Green) Nathalie Fontanet (FDP) Kaspar Becker (Centre) Andrea Bettiga (FDP) Markus Heer (SP) Marianne Lienhard (SVP) Mario Cavigelli (Centre) Jon Domenic Parolini (Centre) Peter Peyer (SP) Christian Rathgeb (FDP) Nathalie Barthoulot (SP) Rosalie Beuret Siess (SP) Martial Courtet (CVP) Jacques Gerber (FDP) Fabian Peter (FDP) Marcel Schwerzmann (Ind) Paul Winiker (SVP) Reto Wyss (Centre) Laurent Favre (FDP) Crystel Graf (FDP) Alain Ribaux (FDP) Florence Nater (SP) Michèle Blöchliger (SVP) Othmar Filliger (Centre) Karin Kayser-Frutschi (Centre) Therese Rotzer-Mathyer (Centre) Res Schmid (SVP) Peter Truttmann (GLP) Josef Hess (independent) Cornelia Kaufmann-Hurschler(CVP) Christian Schäli (CSP OW) Daniel Wyler (SVP) Martin Kessler (FDP) Patrick Strasser (SP) Dino Tamagni (SVP) Walter Vogelsanger (SP) Herbert Huwiler (SVP) Kaspar Michel (FDP) Sandro Patierno (Centre) Michael Stähli (Centre) Petra Steimen-Rickenbacher (FDP) Peter Hodel (FDP) Sandra Kolly-Altermatt (Centre) Susanne Schaffner (SP) Brigit Wyss (Green) Laura Bucher (SP) Bruno Damann (Centre) Susanne Hartmann (Centre) Stefan Kölliker (SVP) Marc Mächler (FDP) Beat Tinner (FDP) Dominik Diezi (Centre) Monika Knill-Kradolfer (SVP) Urs Martin (SVP) Walter Schönholzer (FDP) Manuele Bertoli (SP) Raffaele De Rosa (Centre) Norman Gobbi (Lega) Christian Vitta (FDP) Christian Arnold (SVP) Urban Camenzind (Centre) Daniel Furrer (Centre) Beat Jörg (Centre) Dimitri Moretti (SP) Roger Nager (FDP) Christophe Darbellay (Centre) Frédéric Favre (FDP) Mathias Reynard (SP) Franz Ruppen (SVP) Frédéric Borloz (FDP) Valérie Dittli (centre) Nuria Gorrite (SP) Isabelle Moret (FDP) Rebecca Ruiz (SP) Vassilis Venizelos (Green) Andreas Hostettler (FDP) Stephan Schleiss (SVP) Heinz Tännler (SVP) Silvia Thalmann-Gut (Centre) Beat Villiger (Centre) Florian Weber (FDP) Mario Fehr (independent) Martin Neukom (Green) Natalie Rickli (SVP) Silvia Steiner (Centre) Ernst Stocker (SVP) Carmen Walker Späh (FDP) Viola Amherd (Centre) Guy Parmelin (SVP) Ignazio Cassis (FDP) Karin Keller-Sutter (FDP) Albert Rösti (SVP) Elisabeth Baume-Schneider (SP)