You don't get stronger in the gym. You get stronger while you rest after working out and your muscles repair. If you work them too much, they'll stop growing.
As for whether you can train the same groups repeatedly during a week, it depends on how long you've been lifting for. In general, it's ok for someone new to lifting to work one group twice a week since they won't be lifting that heavy. People at a more intermediate or advanced stage should only work a muscle group once a week as they'll be lifting heavier and putting the muscles under more stress so require longer recovery time. Muscles aching is not a sign of growth or of how well you've worked out so the lack of pain is not a signal that your muscles are ready to work again. Aching muscles are just a sign that you've done something that they aren't used to. The longer you follow a routine for, the more your muscles will adapt and the less they will ache post workout. They still need time to grow though. Eventually your body will have adapted to the extent that it'll stop growing, which is when you'll need to change your routine and do something to shock them back in to growth ie by doing something they aren't used to doing.
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