Yes, that's big capacitor is the main one which will have up to 400-420v DC on it while the power supply runs.
Right near it, there's a "bleeder resistor"which slowly discharges the capacitor as soon as the psu is turned off. However, sometimes these resistors aren't installed or they're broken, so it's possible to have high voltage on that capacitor after psu is shut down. So NEVER assume that capacitor is discharged.
Safest would be to get a multimeter and MEASURE the voltage on its terminals before you get close to it. If there's more than around 10-20v on it, discharge it. You COULD just use a screwdriver and make a short circuit between the two terminals, but if there's a lot of energy in the capacitor you can damage the screwdriver and in rarer cases even the circuit board if you just short the capacitor with a screwdriver.
Safer method would be to get a resistor (let's say 100 ohm 1w or higher) and carefully connect the resistor between the terminals for a few seconds and then measure voltage again with multimeter.
regarding color on polymer capacitors - it's mostly related to who manufacturers them, some company may prefer RED (for example nichicon), other may prefer light blue (I think teapo for example), others use the plain black or gray. You can often tell which manufacturer is by the series - for example FP is an indicative of "nichicon fp series", fp being short for "functional polymer" or something like that.
In one of your posts, there's one with FP and 49cr written on it - FP is series, 49cr is factory code, like manufacturing date or extra series information, and then there's 2 numbers ... the one ending with 1 is the capacitance in short form ... like for example 471 means 47 x 10
1 = 470uF , and the last line 16 means voltage, 16v.
In another picture there's some light blue capacitors, those are made by Nippon Chemi Con / United Chemi Con - i can tell that because of the tiny "hat", the small rectangle like thing over the text
Here's an example (click on picture to see what i mean) :
https://www.digikey.com/product-detail/en/united-chemi-con/APSC6R3ELL152MJB5S/565-3229-ND/1826693In your picture, you easily see the capacitance (330uF - in long form because the capacitor is wide enough to fit more than 3 digits), and 16 which means voltage rating. The series may be determined (or not) from the letter and numbers above capacitance.
There's usually enough room on these capacitors to have capacitance and voltage written on them
Yes, there's differences between them, like ripple current values, esr etc, but in power supplies you want polymer with very low esr and high current ripple so there's a bunch of series with similar values, therefore you don't have to use the exact series from the exact maker.
Don't mess with the main capacitor, won't make any difference and it's from a quality manufacturer.