AFor example, is the Wilton tip 1M the same as Atecco or Martha Stewart brands? Martha Stewart had a "tutorial" on a certain style using a certain tip and I was curious if my Wilton tip would be the same. Thanks!

no they are all different

I have fround from time to time that there is a slight difference. 

For the most part they are the same, but some differences cvan ocvcure.

I remember that Ateco was different  than Wilton and of course, any from England are numbered differently than those from US companies.