From the AC:CF Wikispace --
Axe: 400 bells from Nook's shop
Silver Axe: Serena (after throwing an axe into the town fountain)
Golden Axe: Serena (after throwing an axe into the town fountain)
The difference: Silver Axes will never break. Golden Axes will also never break, and cut trees down much faster.
How to get a Golden/Silver Axe:
Getting the Golden and Silver Axes can be very difficult and time-consuming. To start, begin by donating 500,000 bells to your town fund. This will allow your town to acquire the fountain reward. After your fountain is built, buy a normal axe from Tom Nook's store and head over to the fountain. Go directly to the bottom of the fountain where the opening in the gate is and press "A", as if you were chopping a tree. By doing this, you will throw your axe into the fountain and call forth Serena, a Chihuahua goddess. She will appear on the top of the fountain and ask you what kind of axe you threw in. You must be honest or you won't get your axe back. Pick the "a normal axe" option. Then she'll be glad you told the truth. From there, continue with her questions until you finally attain the golden and silver axes. (Please note that Serena might run out of axes occasionally and repeating this whole process until you get your axes can take a very long time.)
Net: 500 bells from Nook's shop
Silver Net: 500 bells from Nook's shop (after level 2 upgrade)
Golden Net: From Tortimer after catching every bug.
The difference: The Silver Net is a bit bigger than the normal net, while the golden net makes catching bugs 'a breeze' whilst being bigger than the Silver Net.
Shovel: 500 bells from Nook's shop
Silver Shovel: Resetti Surveillance Center
Golden Shovel: Bury a Shovel for 24 hours.
The difference: A Silver Shovel gives you a 10% chance for more bells when you're smacking rocks. The Golden Shovel allows you to plant Bell trees.
Fishing Rod: 500 bells from Nook's shop
Silver Rod: 500 bells from Nook's shop (after level 2 upgrade)
Golden Rod: From Tortimer after catching every fish.
The difference: Silver Rods have better lures than normal rods, making fishing a bit easier. Golden Rods 'is a real fish magnet!' plus makes the fish hold onto the bait for a little bit longer.
Slingshot: 500 bells from Nook's Shop
Silver Slingshot: 500 bells from Nook's Shop (after level 2 upgrade)
Golden Slingshot: Balloon (after shooting at least eight balloons)
The difference: The Silver Slingshot fires two pebbles instead of one, while the Golden Slingshot fires three.
Watering Can: 500 bells from Nook's shop
Silver Watering Can: From Nook's Shop after buying 50 bags of seeds
Golden Watering Can: From Town Hall after maintaining a perfect town for 15 days straight.
The difference: The Silver Watering Can has a wider radius for sprinkling water and can restore wilted Red Turnips. The Golden can has no information revealed but is most likely to have the same attribute as the Golden Can in Wild World... the ability to create Golden Roses.