I'm having to hold and press links in Safari to open the pages - I used to just touch it and it would open. I prefer the latter but how do change it back? I can't find any info online (probably because I don't know the correct terminology to perform an effective search).
Have you checked your settings in General > Accessibilities? For most people, most of the options should be disabled (except for shaking the screen to undo an action which is by preference).
I have a possibility. Are General > Accessibility > Touch Accommodations > Touch Accommodations + Hold Duration both turned on? Because they make it so that you have to hold on the screen in order to register a touch. That seems to fit your context because they should be off in general.