A good overview of how different versions of Penn World Table correspond to each other is given by Section 2.1 of Pinkovskiy and Sala-i-Marin (2016).
Its Section 2.2 is also useful for whether you should use PWT or World Development Indicators for real GDP per capita.
The major change from Version 7 to 8 was, if I understand correctly, a response to the critique by Johnson et al. (2009).
Below is my own rough summary of how real GDP per capita is computed up to Version 7: For more detailed accounts, see Johnson et al. (2009).
1. Collect data of prices of hundreds of identically specified goods and services prevailing in each "benchmark" country (this is done by the United Nations International Comparison Program, or ICP).
The PWT version 6 uses the 1993 ICP data. As the 2005 ICP data is now released, GDP figures in international dollars are likely to change. See Arvind Subramanian's article on Dani Rodrik's blog.
2. Obtain PPPs for the benchmark countries by comparing the prices of each good and service.
3. Use capital city price surveys by United Nations International City Service Commission, Employment Conditions Abroad (a British firm), and the US State Department, to estimate PPPs for a wider range of countries.
4. By regressing PPPs obtained in step 2 on PPPs obtained in step 3 for the sample of benchmark countries, PPPs for non-benchmark countries are estimated based on their PPP estimates obtained in step 3.
5. Use PPPs to convert the countries' national currency expenditures (from national accounts) to a common currency unit.
Steps 1-5 were carried out for the base year (1985 for PWT version 5; 1996 for PWT version 6.1).
6. Real GDP per capita in PPP for other years is obtained by applying the growth rates from the constant-price national accounts series to the base-year real GDP per capita.
See pages 329, 341-4 of Robert Summers and Alan Heston (1991) "The Penn World Table (Mark 5): An Expanded Set of International Comparisons, 1950-1988" Quarterly Journal of Economics, 106, pp.327-368.