basically, if its the same note, just add the duration to the note without picking it, ie. a quarter note tied to another quarter note would be held for two beats.

not technically the same thing, but if its tied to a different note, its a slur, which means either pull off, hammer on, or slide to the note. but in tabs this is generally not the case.
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With tied notes you add the value of each note together.
Say you have a quarter note and a whole note and they're tied, that comes out to a continuous 5 beats rather than the one beat and then the four beats.
It's the same note without picking/hammering/pulling it to extend a note to an abnormal length or add vibrato (like I do) after a certain length. For example, I would have a normal note as a half note then have a quarter note tied to it with vibrato on it so the vibrato starts after the half note is played without it but it is not picked again.