I will try my best to ans your question here.
CDS Spread is the spread that the buyer pays the seller periodically.
CDS Coupon is the fixed coupon of either 100 or 500 bps. (This is set by the standardization of North American corporate CDS)
Because of the standardized coupons, this is why we have to pay upfront premium.
For instance, quoted CDS spread is 200 bps and CDS coupon is 100 bps with maturity of 5 years, to find the upfront premium you just plugin the numbers into the formula. (This formula is just the approximation in percentage terms)
=> Upfront premium % ≈ (200bps - 100bps)x5
There is the upfront premium because of the standardization of the coupon. Therefore, you now pay 100bps per year as a standard premium with the upfront premium. Otherwise you would have just paid the 200bps CDS spread per year with no upfront premium.
Another formula as you mentioned earlier is not in the percentage terms. (Upfront payment = PV of protection leg - PV of premium leg.)
Hope this helps.