An image file is made of pixels, the smallest discrete units of digital information it contains. PPI describes how densely those pixels pack into an inch when the file is displayed or sent to a printer. DPI describes the printer's own output: how many physical ink dots it lays per inch, sometimes several dots per single pixel depending on the printer technology.
Effective DPI comes from the same division used everywhere else on this site: pixel count on an edge, divided by the inches that edge is printed at. A 3,000-pixel edge printed at 10 inches works out to 300 effective DPI. Feed that same file to a printer rated at a different physical DPI and the printer still reproduces it at 300 dots per inch of image detail; the printer's own rated DPI is a separate, fixed hardware number.
The DPI Calculator applies this exact division to your own pixel dimensions and print size.
In casual usage, yes. 72 PPI is the old screen standard carried over from early Mac monitors, and it was never a print resolution. At 72 PPI, a 4x6 print would only have 288 x 432 pixels, which prints as a blurry smear at normal photo size.
The image's PPI is the number you set; the printer's DPI is a hardware spec you generally cannot change. Set a file to 300 PPI at the intended print dimensions and the printer takes it from there, at whatever DPI it is rated for, typically 300 to 1200.
Start with what DPI measures on its own if the printer side still feels fuzzy, or jump to finding your image's current pixel count to apply this directly.
In practice, yes. Setting an image to 300 PPI and sending it to a 300 DPI printer maps one pixel to one printer-dot position.
In common usage, yes. 72 PPI is the standard for web and screen display and is far too low for printing at normal photo sizes.
For print workflow purposes, they refer to the same density. 100 falls well below the 300 standard for photo printing.
Yes, in workflow terms. 150 is acceptable for large prints viewed from several feet away, such as posters or banners.