Yes, a second line means positive! Yes, I have had tests appear lighter. I worked in a family planning clinic with both of my pregnancies, so I had access to daily testing.
HCG, the hormone detected with pregnancy tests, is detectable once implantation occurs (usually 7-9 days post-CONCEPTION... not necessarily post-ovulation). It doubles every 36-48 hours, peaks at 8-10 weeks, then declines to lower levels the rest of pregnancy. It is most accurately measured with serum (blood) tests. It is very common for a positive urine pregnancy test to be faint in early pregnancy because of the lower levels of HCG. The line will darken as HCG increases, which yes you want to happen, but the urine tests do not provide a quantitative measurement.
As for the line being lighter today... are you comparing the test last night with the test this AM... a side by side comparison? The urine tests should have a timeframe for reading. For example, the tests used at the clinic are read after 5 minuts. Results read after 10 minutes are considered invalid. This is because the second line (positive line) darkens over time even in negative tests. So, a test that is negative may develop a faint line as the tests ages.
Take care!