There have been 10 separate NBA players to win regular season Most Valuable Player and Finals Most Valuable Player in the same season starting with Willis Reed in 1970. Finals MVP wasn't introduced until the 68-69 season.

Michael Jordan accomplished the feat four separate times, while Larry Bird and LeBron James each did it twice.

1970: Willis Reed
1971: Kareem Abdul-Jabbar
1983: Moses Malone
1984, 1986: Larry Bird
1987: Magic Johnson
1991, 1992, 1996, 1998: Michael Jordan
1994: Hakeem Olajuwon
2000: Shaquille O'Neal
2003: Tim Duncan
2012, 2013: LeBron James

The regular season MVP has won the championship, but not won Finals MVP in eight seasons (* for season where no MVP given):
1957: Bob Cousy*
1961: Bill Russell*
1962: Bill Russell*
1963: Bill Russell*
1965: Bill Russell*
1967: Wilt Chamberlain*
1980: Kareem Abdul-Jabbar
2015: Stephen Curry

The regular season MVP has reached The Finals, but lost in 10 separate seasons:
1958: Bill Russell
1974: Kareem Abdul-Jabbar
1982: Moses Malone
1985: Larry Bird
1989: Magic Johnson
1993: Charles Barkley
1997: Karl Malone
2001: Allen Iverson
2008: Kobe Bryant
2016: Stephen Curry