Terminology

As English translations for the German terms, I will use the terms being used in Great Britain and Ireland.

Some special terms are explained here:

Signal Aspect	German railway signals are classified into various sections, such as main and distant signals, shunting signals, point signals, etc. Every signal aspect has an identifier that is formed of an abbreviation of the group the signal belongs to (e.g. Hp for Hauptsignal) and a number (e.g. Hp 0: stop). The aspect is, exactly speaking, the actual appearance of the signal (e.g., a red light). The aspect determines the meaning of the signal, (e.g.: stop)
Signal	In German railway terminology not only semaphores or colour light signals, but also boards, markers, plates, train head and tail lights, and sounds such as a whistle are called 'Signale'.
Train Movement vs. Shunting Movement	A train movement is a timetable-scheduled movement as opposed to a shunting movement, which is governed individually, i.e. by special orders. For exact rules, see German signalling basics

[Obsolete]	Identifies something ruled out recently, which nevertheless may still be seen

British vs. American terms

Here I will give just some special translations. Within this site, I will use British/Irish terms unless otherwise noted.

Some special notes seem to be necessary regarding points (thanks to Michael J. Stokes for directing my attention to this).
Deutsch	British	US	Notes
Weiche	Points	Switch, Turnout	in BrE 'Points' refer to the whole track changing device (AmE=Switch)
Zunge	Point, Point Blade	Point	the moving rails in points / in a switch, lit. 'Tongue'
Herzstück	Frog		lit. 'Heart piece'
gegen die Spitze	Facing Points
vom Herzstück	Trailing Points		lit. 'From Heart piece (Frog)'
eine Weiche aufschneiden	Split Points		lit. 'to Cut Open the Points'
einfache Kreuzungsweiche (EKW)	Single Slip Points	Single Slip Switch
doppelte Kreuzungsweiche (DKW)	Double Slip Points	Double Slip Switch
Rückfallweiche	Spring-Loaded Points	Spring-Loaded Switch
Kreuzung	(Diamond) Crossing