Do all types of braces do the same job to straighten teeth? I need them but I don't want to get the ones with brackets

No, they do not. Invisalign (which is technically not "braces" but rather a removable appliance) can work wonders in straightening out malpositioned teeth. But any orthodontist will tell you that Invisalign does not provide the fine control that brackets and wires do. Consult with a local orthodontist to see which system will work best for your smile.
LicensedOrthodontist. If you do not feel comfortable with braces that show, ask about other options like Lingual Braces or Invisalign which are hidden or removable braces. It is very important that when researching the types of braces that are available on the market see a licensed Orthodontist.