Inadmissible grounds make a person inadmissible to the US
Removal ground make a person removable from the US
In some situations inadmissible grounds may form the basis for making a person removable.
If you have a particular situation you set up a consultation with an attorney that practices immigration law.
Great question. An LPR can be removed for being inadmissible if they depart the U.S. and return and DHS considers them seeking a new admission pursuant to INA 101(a)(13)(C). See also Vartelas v. Holder. The charges on that Notice to Appear would be as an arriving alien and subject to grounds of inadmissibility under INA 212. An LPR can be deported after admission for various offenses found in INA 237(a).