As usual, I can only speak for AE (although, I suspect that this is similar in other English-speaking countries).
Here, we do distinguish between arrests with warrants and arrests without warrants (typically called "warrantless arrests"), but we do not have any particular terms (comparable to "verhaften" and "festnehmen") to designate that distinction. Whatever your ultimate choice of words may be, an ambiguity remains until you state clearly whether the arrest (or whatever) was done with a warrant or without one. So just say "to arrest pursuant to a warrant," or "to conduct a warrantless arrest," or something along that line...
to arrest = full-scale arrest, implicates certain constitutional rights, but can be had with and without a warrant (if without a warrant, very specific circumstances must exist for the arrest to be valid)
to seize = more ambiguous, with or without a warrant, typically not used for persons (but possible)
to imprison = NOT a possibility; a person is imprisoned only as a result of a court's judgment and committment order; refers to the actual act of putting someone into prison, as part of a prison sentence
to take into custody = probably the most synonymous with "to arrest"; again, it says nothing about whether a warrant exists
to detain = can refer to a brief, temporary stop that is short of an actual arrest; this distinction bears on certain constitutional issues concerning what the police may or may not do during that detention; has no real bearing on the warrant question, but is not particularly common in legal usage; of course, "to detain" also implicates detentions in a much broader, non-police sense (see Guantanamo Bay, for instance).