Can I use my 60 watt adapter to charge my iphone or does it have to be 61 watt?

That won't be a problem. However if it's not actually an Apple-made charger be careful as some imported third-party chargers have been found to be unreliable. I shouldn't leave it unattended. If it's made by Apple it's perfectly safe.

There's no practical difference between 60 and 61, but you can use a lower power charger to charge any device, it will just take longer.