Question

why does the constitution specify different ways to determain the number of members for the House and for the Senate?

Answer 1

It was a compromise. Some people wanted each state to have the same number of votes in the legislature. So we have the Senate with two Senators from each state. Others wanted the voters represented, regardless of whether they lived in a small or large state. So we have the House, with a representative for each district with approximately the same population.