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. 
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' 
Shovel: 500 bells from Nook's shop 
Silver Shovel: Resetti Surveillance Center 
Golden Shovel: Bury a Shovel for four days. 
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!' 
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 bullets 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. The Golden can.. well it doesn't say the perks, but I'm pretty sure it severely helps the success rate of plants growing.