That 2000 figure was from memory without checking. Drawing upon the excellent Encyclopedia Astronautica website, I get a different number but I think his figures aren't quite complete.

Both of these boosters are part of the Russian R-7 family, which was derived from the world's first operational ICBM. They never built that many of the R-7 ICBMs because better technology came along, just as it did with the Atlas and Titan I ICBMs. From the entry about the upgraded R-7A ICBM, the operational version:

The missiles on the four pads were programmed to hit New York, Washington, Los Angeles, and Chicago. During the Cuban missile crisis (11 September to 21 November 1962), an R-7A with a live thermonuclear weapon was held in readiness on pad LC41 for launch on the United States with an 8 to 12 hour reaction time from the go order. This was the only time an R-7A was actually armed with a nuclear warhead during its service life (early Soviet doctrine was that the warheads be stored and controlled separately).

The R-7A, with its slow reaction time and vulnerability to enemy counter-strikes, was withdrawn as more modern ICBM's were deployed in the 1960's. LC 41 was withdrawn from ICBM service in 1963 and converted to a space launch pad for R-7-derived launch vehicles. LC16 and the two pads at LC43 continued in service until the R-7A was withdrawn from military service in 1968. LC 16 was cannibalised to rebuild the LC1 at Baikonur, and LC43 was converted to use as a space launch facility.

The base R-7 was used to launch some of Russia's earliest satellites. It was upgraded to the SL-03 Vostok booster a few years later.

SL-04 Soyuz 11A511:
Launches: 30. Failures: 2. Success Rate: 93.33% pct. First Launch Date: 28 November 1966. Last Launch Date: 24 May 1975

SL-04 Soyuz 11A511L:
Launches: 3. Success Rate: 100.00%

SL-04 Soyuz 11A511M:
Launches: 8. Success Rate: 100.00% pct

SL-04 Soyuz 11A511U:
Launches: 699. Failures: 18. Success Rate: 97.42% pct. First Launch Date: 18 May 1973. Last Launch Date: 02 February 2003

SL-04 Soyuz 11A511U2:
Launches: 92. Failures: 2. Success Rate: 97.83% pct. First Launch Date: 23 December 1982. Last Launch Date: 03 September 1995

SL-04 Soyuz FG:

Launches: 4. Success Rate: 100.00% pct

SL-06 Molniya 8K78:

Launches: 27. Failures: 15. Success Rate: 44.44% pct. First Launch Date: 20 January 1960. Last Launch Date: 30 June 1970.

SL-06 Molniya 8K78M:

Improved Molniya, in variants with Blocks ML, 2BL, or SO-L third stages according to payload. Launches: 288. Failures: 19. Success Rate: 93.40% pct. First Launch Date: 19 February 1964. Last Launch Date: 24 December 2002.

Launches / Failures / Success Rate
SL-04 11A511: <T> 30 / 2 / 93.33%
SL-04 11A511L: <t> 3 / 0 / 100%
SL-04 11A511M: <t> 8 / 0 / 100%
SL-04 11A511U: <t> 699 / 18 / 97.42%
SL-04 11A511U2: <t> 92 / 2 / 97.83%
SL-04 Soyuz FG: <t> 4 / 0 / 100%
Subtotals: <t> 842 / 22 / 97.39%

SL-06 8K78: <t> 27 / 15 / 44.44%
SL-06 8K78M:<t> 288 / 19 / 93.4%
Subtotals: <t> 315 / 31 / 90.15%

Totals: 1157 / 53 / 95.42%

However, that number of launches doesn't agree with their earlier statement here:

By the year 2000 over 1,628 had been launched with an unmatched success rate of 97.5% for production models. Improved models providing commercial launch services for international customers are even now entering service. It appears the R-7 will easily be in service past the 50th anniversary of its first launch.

There weren't that many of the earlier SL-01 and SL-03 boosters to account for the discrepancy. The fact remains that more of the R-7 derivative space boosters have been launched than any other type in the world and they enjoy a very high success rate compared to other boosters. The Molniya booster is more complicated than the Soyuz and has a higher failure rate to reflect that, especially with the first versions.