Muscle pump from resistance training is caused by the increased blood flow into the muscle to supply needed oxygen. That's why it subsides after a while. It's a sign that you are making a muscle work hard.
Muscle "burn" (usually from high-rep exercises or HIIT) is caused by hydrogen ions (not lactic acid). It's another sign that you have worked hard, but means nothing more.
For strength-maintenance and strength-building you need to create micro- tears in your muscle fibers. This can sometimes result in muscle soreness for a day or two. It's a good sign of the inflammation needed for muscle repair.
The repair is what builds strength. That's why it's never a bad idea to have a 20-25 gm. protein shake as a meal (we like to make it with a banana) shortly after an hour of resistance exertion. It's also why it's smart to recover for 48 hours or so before pushing heavy weights again. (We advocate "active recovery" days in the form of calisthenics and cardio.)
There is an exception, though, to the 48-hour rule. That is when people separate their resistance days between legs and upper body. That works for some people but I do not like it.