The result is that they are top of one table, bottom off the other.
Neil Lennon's side mean to get to work on rectifying their Group H disadvantage tomorrow when they face Ajax, despite the fact Saturday's 1-1 draw with Hibs at Easter Road has left the manager with even more big decisions to make. Who replaces suspended captain Scott Brown was giving him enough to contemplate.
But the hamstring injury sustained by Kris Commons in the first half against Hibs - he was replaced by James Forrest, who equalised Paul Heffernan's opener scored from an offside position - means a more comprehensive reshuffle will be required.
Having made a dash to watch Frank de Boer's side draw 1-1 with Twente Enschede immediately after his own team's match in Edinburgh, Lennon is now checking on how important players like Forrest and Joe Ledley, both of whom are returning after lengthy lay-offs with injury and illness, have come through Saturday's bruising contest.
Emilio Izaguirre - who was confined to bed after returning from international duty with Honduras suffering from a virus - and another casualty of national service, Sweden's Mikael Lustig, will also be assessed before Lennon finalises his starting XI.
The manager is facing one of the toughest selections of his career, but is doing all in his power to try and play up the positives in an attempt to reduce the psychological threat posed by the negatives.
Forrest's solo goal on Saturday was his first since he hit the winner against Shakhter Karagandy to take the club into the group stage, and the manner of the goal reminded everyone what a special talent he is and what a threat he can be to the Dutch.
Set to start his first Champions League game since the play-off - he missed the trip to the San Siro and got only the closing stages of the game against Barcelona - the 22-year-old will be a key man in Lennon's plans.
The Hoops boss said: "We will have to set the team up a little bit differently, in terms of personnel and the shape. But, to have James back is great for us.
"He did his rehab during the international break. I spoke to him on Friday and he still feels he is not 100%.
"His conditioning was curtailed in pre-season and, obviously, with the virus he had, he has lost a lot of weight. Now he is starting to look more like himself.
"We were looking at giving him 20 minutes or half an hour on Saturday, but, because of what happened to Kris, he had to go on much sooner.
"He looked a lot better than he had done, and he has looked great in training.
"Psychologically, he has been a bit worried that he is not doing himself justice. But, we have no worries on that aspect with him."
Judging who is ready, both mentally and physically, to give their all in a crunch game such as tomorrow's is a big part of Lennon's job.
The loss of leader Brown - perhaps for three group games, though plans to appeal his extended punishment within Uefa's five-working-days timescale are well advanced - and now main creator, Commons, means others have to step up to the plate.
Men like Nir Biton have had their chances to integrate into the side restricted by call-ups for international duty.
Others, like Beram Kayal, have had to be patient as they have waited to get back into the starting line-up as others have simply been playing better and more consistently than them.
Ledley - with the spectre of a contract running out and talks on a new one not making any great strides - knows that a commanding performance in a top European game where he can show that fitness issues are not a factor will strengthen his negotiating position considerably.
Lennon will ignore all of the above, and simply select who he believes can best serve the side on the night.
"Nir has been away with Israel, but has not played any games with them during that time," said the Hoops boss.
"Beram is just back from injury, as is Joe. So, I will have to see how we are today.
"Obviously, we have got big assets to find for this game."
Kayal would appear to be ahead of Biton and Ledley for the vacant holding midfield role alongside Charlie Mulgrew.
But Ledley is a player Lennon trusts implicitly. And, if his 25-minute run out as a replacement for Kayal at the weekend has done enough to convince the manager he has shaken off the rust from a four-week lay-off and is managing his long-standing hip problem, he could jump to the top of the queue for a start.
"Joe looked all right when he came on against Hibs," said Lennon, who was also impressed by rookie right-back, Darnell Fisher.
"But he had not kicked a ball for over a month before that.
"He only trained on Friday, and we probably threw him on sooner than we would have expected to. But I was pleased with him."
Lennon is only too aware de Boer will be studying Celtic's personnel dilemma closely and will be ready to try and exploit any weakness.
Likewise, the Parkhead manager has taken every opportunity to pinpoint where the Eredivisie champions may be vulnerable.
"I went over to watch Ajax again on Saturday night because I wanted to see them as close to the game here as I could," explained Lennon.
"They are a good team and will cause us problems. There is no question about that. This is not a foregone conclusion, by any means.
"This is Ajax, the Dutch champions who finished third in what was called the 'Group of Death' last year. They will give us as many problems as any other team in this group."