Answers:
强势意味着低电阻。弱意味着高抵抗力。当然，低和高是相对术语，强和弱也是如此。必须从上下文中推断出此关系的参考。
甲强或低电阻上拉/下拉电阻是好事，因为所形成的负载电容（通常，输入栅极电容，并且PCB迹线电容）时间常数是小的，所以上升/下降时间将是短的。
甲强上拉/下拉电阻是好的，因为从非预期的耦合和EMI噪声电流将导致更小的噪声电压。（想想欧姆定律）
一个弱或高电阻上拉/下拉电阻是好的，因为它不会从驱动电路对电阻器的工作需要多大的电流。因此，电池使用寿命更长，零件可以更小，并且不会变热。
当然，您通常需要所有这些东西，但电阻器不能兼而有之。有关的讨论强与弱通常是澄清，其中这些问题（或者其他）是为特定的应用更为重要。
A "weak" pull resistor is usually a high value resistor that only allows a small amount of current through, and can quickly be overwritten, but takes longer to reassert itself.
A "strong" pull resistor is usually a low value resistor, allows more current through, takes longer to be overwritten, but can quickly reassert a line.
They are completely relative to your needs, not just other pull resistors like internal ones.
In your button scenario, the time it takes to switch from one state to the other isn't important, so weak vs strong doesn't apply there. But weak vs strong does apply in the practical matter of Current Consumption. A strong pull resistor would, when the button is pressed, cause a large drain of current from vcc through the resistor to ground. A weak pull resistor would cause a small drain of current. Theoretically any resistor would work, but for practical purposes, a weak resistor is used because unnecessary high current drains can cause issues and can easily be avoided by sizing the resistor correctly.
Does "strong" vs "weak" only apply when one such resistor is being compared to other resistances in the circuit, such as an internal pull-down resistor?
Yes, this is exactly it. Strong and weak simply refer to the relative drive strength of the component. A pull up/down resistor's value has no association to whether it is strong or weak. Only in knowing the context of the other connections to the net can you determine if a pull-up is strong or weak.
There are other things to consider when selecting the value of a pull-up or pull-down. For example, depending on the capacitance of the circuit, too week of a pull-up/down will limit how quickly the voltage change occurs. On the other hand, too strong of a pull-up/down will draw excessive current through whatever is trying to pull the other way. These are often considerations in selecting the pull-ups for an I2C (open drain) bus, for example.
However, the place I see "weak pull-ups" typically used is inside microcontroller chips, typically on I/O pins. These are mainly used to guarantee that an input won't float if not connected. The pull-ups are weak both to limit their effect on the external circuitry and to limit the power dissipated inside the chip.
When you put a large resistance for ground coupling, the voltage developed across it would prevent the node from getting to ground potential. On the other hand, if you put small resistance to the ground, the node potential would be more close to V(gnd). If R(gnd) is high, it would not be able to pull down your node to zero potential. So, you can consider this as "weak" pull down, and vice-versa. Of course, this is just for comparison purpose only (with other components in your circuit)