First, the pigtail adapter takes care of everything you need to do, There is nothing for you to worry about with one slight exception I'll cover
Down from 50 amp: Your house likely has 150 or 200 amp service this is the MAXIMUM you can draw before CLICK goes the main breaker.. a standard wall outlet with two parallel slots (both straight) is 15 amps, Try to draw 18 and CLICK goes the breaker.. one with a "T" shaped neutral is 20 amps. try to draw 25 and CLICK goes the breaker (Assuming they did not put a 15 amp breaker on it, I sometimes do use 15/20 amp outlets on 15 amp circuits..
A 120 watt lamp is 1 amp.. This means it will draw one amp. no more.. Even if it is plugged into a 20 amp circuit it only draws one amp.
Your RV is like that lamp, IT can only draw a max of 30 amps. then CLICK the main breaker in the RV trips. So if you plug into a 50 amp outlet using a proper adapter.. Well, you only get 30 amps.
The 50 amp outlet has 4 wires, the 30 only 3, so what do they do with the 4th wire? NOTHING, it's not connected.. It is ignored inside the adapter.
Now that we have coverd 50 amps let's tackle 15/20 amp. And then one final caution.
15/20 amp outlets the wiring is identical to the 30, only the plugs are different and of course the capacity.. So you must be very careful with how much load you put on the circuit.. Try to draw 25 amps and CLICK. nothign as the breaker trips.. No other special concerns other than max current.
NOTE: My converter can draw from 1 to 10 amps depending on battery state of charge and other things.. Bear this in mind.. When I first plug in it is best not to run the A/C for a couple hours on 20 amps.
Finally the caution....
There are some outlets other than the TT-30 which your 30 amp trailer plug will fit into nicely.. You often find outlets of this type on a back porch, or in a garage.. They were installed for a Cloths Dryer, or Air Compressor, or other high power 240 volt Device and will let a lot of the magic smoke out of your expensive electronics.. As we all know electronics operate on Magic Smoke, let it out and they no longer function.. In fact they can ignite. (not good).
A Progressive Industries HW-30C or PT-30C will protect you should you accidentally plug into one of these.. I recommend the HW (Hard Wired) as you do not forget those. TRC makes a SURGE GUARD product line, The ones with the LCD display also do the job but I like PI better, lifetime warranty v/s 1 year on the TRC.