What is the difference between “px”, “dip”, “dp” and “sp”?

From the Android Developer Documentation:

1. px
   > Pixels – corresponds to actual pixels on the screen.
2. in
   > Inches – based on the physical size of the screen.
   > 1 Inch = 2.54 centimeters
3. mm
   > Millimeters – based on the physical size of the screen.
4. pt
   > Points – 1/72 of an inch based on the physical size of the screen.
5. dp or dip
   > Density-independent Pixels – an abstract unit that is based on the physical density of the screen. These units are relative to a 160 dpi screen, so one dp is one pixel on a 160 dpi screen. The ratio of dp-to-pixel will change with the screen density, but not necessarily in direct proportion. Note: The compiler accepts both “dip” and “dp”, though “dp” is more consistent with “sp”.
6. sp
   > Scaleable Pixels OR scale-independent pixels – this is like the dp unit, but it is also scaled by the user’s font size preference. It is recommended you use this unit when specifying font sizes, so they will be adjusted for both the screen density and the user’s preference. Note, the Android documentation is inconsistent on what sp actually stands for, one doc says “scale-independent pixels”, the other says “scaleable pixels”.

From Understanding Density Independence In Android:

Density Bucket	Screen Density	Physical Size	Pixel Size
ldpi	120 dpi	0.5 x 0.5 in	0.5 in * 120 dpi = 60×60 px
mdpi	160 dpi	0.5 x 0.5 in	0.5 in * 160 dpi = 80×80 px
hdpi	240 dpi	0.5 x 0.5 in	0.5 in * 240 dpi = 120×120 px
xhdpi	320 dpi	0.5 x 0.5 in	0.5 in * 320 dpi = 160×160 px
xxhdpi	480 dpi	0.5 x 0.5 in	0.5 in * 480 dpi = 240×240 px
xxxhdpi	640 dpi	0.5 x 0.5 in	0.5 in * 640 dpi = 320×320 px

Unit	Description	Units Per Physical Inch	Density Independent?	Same Physical Size On Every Screen?
px	Pixels	Varies	No	No
in	Inches	1	Yes	Yes
mm	Millimeters	25.4	Yes	Yes
pt	Points	72	Yes	Yes
dp	Density Independent Pixels	~160	Yes	No
sp	Scale Independent Pixels	~160	Yes	No

More info can be also be found in the Google Design Documentation.