They have the same meaning which is "even." They are used when describing something by giving very unusual and surprising examples, but "すら" cannot be used in the subjunctive mode and the conditional mode. "すら" is always used after a noun, but "さえ" is used after a noun/verb/adjective.
I can't even joke around with Ken. He takes things too seriously.
ケンは真面目過ぎる(or物事を真剣に捉えすぎるので)、冗談さえ(orすら)言えない。
ケンは真面目過ぎる(or物事を真剣に捉えすぎるので)、冗談さえ(orすら)言えない。
Meg and her boyfriend are talking about where they would like to go this summer.
- Meg : I'd like to go on a trip to Okinawa. How about you?
沖縄へ旅行に行きたいな。ケイは？ - Kei : Wherever is fine. As long as you are with me, that's all that matters.
どこでもいいよ。メグとさえ一緒にいられれば、それで十分だよ。
---> In this case, it is the conditional mode so you can only use "さえ".
Ken and Leo are talking about what they are going to eat for lunch.
- Ken : I'm so hungry. I didn't eat anything for breakfast. I haven't even had coffee since this morning. Do you want to grab lunch?
朝食をとらなかったので、お腹空いた。朝から、コーヒーさえ(orすら)飲んでいない。ランチに行かない？ - Leo : I would really like to, but I have to finish this report by 1. I'm going to the store to get some snacks.
行きたいけど、一時までにこの報告書を終わらせなきゃいけない。だから、コンビニで何か買うよ。 - Ken : Okay. I'm on my way to Kobe Steak House and it is close to the store so I can keep you company(or tag along with you) for a while.
- Leo : All right. If I have time, I'll grab lunch with you. I could eat a good steak.
うん。時間さえあれば、一緒に(ランチに)行けるのに。美味しいステーキを食べられるのに。
---> In this case, it is the subjunctive mode so you can only use "さえ".