均一 and 均衡: uniform qualities and balance between elements
Compare uniform board thickness and evenly spread paint with balance between two powers and between meals and exercise. Read 均一 and 均衡 without turning balance into identical quantities.
均一 describes an even quality or distribution
均一 (きんいつ) describes a uniform quality or distribution. 「板を均一な厚さに削った。」 means “I planed the boards to a uniform thickness.” Thickness is the quality made uniform. The Japanese 板 does not specify an exact board count.
「絵の具が均一に広がるまで筆を動かした。」 means “I moved the brush until the paint spread evenly.” Here uniformity concerns the paint's spread rather than board thickness. Compare 均一な厚さ with 均一に広がる to find the quality or distribution described.
均衡 relates different elements
均衡 (きんこう) describes balance between elements. 「二つの勢力の均衡が長く保たれていた。」 means “The balance between the two powers had been maintained for years.” The two powers are in the balancing relation. 長く supplies a long duration without a specific number of years.
「食事と運動の均衡を意識して生活する。」 means “I live with attention to balancing meals and exercise.” The balance between meals and exercise is what receives attention. The sentence gives neither equal quantities nor a stated health outcome.
An even quality and a relation of balance
For the boards, thickness is even; for the paint, its spread is even. The powers and the meal-and-exercise example instead present balance between elements. Identify the quality described by 均一 and the elements related by 均衡 rather than reducing both to sameness.
Preserve the long duration of the balance between the powers without inventing a year count. Likewise, attention to balancing meals and exercise does not supply an equal amount or a numerical recommendation. Read the quality or relation that each sentence actually describes.
What is uniform in 「均一な厚さ」, and what is balanced in 「二つの勢力の均衡」?
Show the answer and why
The boards' thickness is uniform, while the two powers stand in a balancing relation. Balance can also concern meals and exercise, but it does not automatically mean equal quantities.