These two terms are used quite frequently when discussing base upgrades and war weight strategies. It is important to understand the difference between these two concepts and their implications. I do not plan to re-hash all of those implications here, as they have already been discussed in more detail in our guides relating to upgrading and war weight. Instead, I will simply provide some definitions.
Before I discuss each concept, I feel the need to define what we mean by towers. Towers are defensive BUILDINGS. This includes point defenses like cannons, archer towers, teslas, and xbows; splash defenses like mortars, wizard towers, and bomb towers; and the unique defenses inferno towers and eagle artillery. It does NOT include any traps or bombs or any non-defensive buildings like barracks, spell factories, or resources buildings
Building out - Building additional towers that have been unlocked, but have not yet been placed.
After each townhall upgrade, several new buildings are unlocked and can be placed once the resources have been acquired. We are ONLY concerned with the new towers. Building out, even with just level 1 towers, has the LARGEST impact on war weight. More so than upgrading current towers (building up). The general rule of thumb is, "don't build it if you cant kill it."
Building up - Upgrading current towers that have already been placed.
While this does impact war weight, any single upgrade is relatively minor. Typically, you are better off upgrading every current tower to max level before building out any new towers. Often, these upgrades will not even register in your indicated war weight as measured through the war base storages.