As said, frame rates do matter with keeping up with a monitor's high refresh rates. Resolution and newer titles can have an impact as graphics cards age and eventually out classed. However games more inline with your card's performance capabilities like csgo and desktop working/browsing environment will be greatly improved compared to 60Hz.
In determining resolution/Hz capabilities of the graphics card, go by the connection types the video card has.
1080p 144Hz = DVI-D Dual Link or DisplayPort
1440p 144Hz = DisplayPort
4096 x 2160 60 Hz = HDMI 2 or DisplayPort
Graphics card specifications hardly ever (if not at all) list information like what you're seeking and is annoying. They just list the absolute max resolution the card is...