They have the same meaning indeed, but their use is a matter of grammar.
They basically all mean "since" (or "from"), but here's how you should use them :
"Depuis" can be used with a noun directly after it, or a time etc..
"Depuis ce jour..." = "Since that day..."
"Depuis que" allows it to be followed by a verb, in the past.
"Depuis que je t'ai rencontré..." = "Since I met you..."
In French, unlike in English, you can't put the verbal group directly after it. You have to use "que".
"Depuis lors" paraphrases a moment we explained earlier. It means "since then"
"Un jour, je me suis perdu en forêt. Depuis lors, je n'y vais plus." = "One day, I got lost in a forest. Since then, I don't go there anymore."
I hope this is useful :)