It would be better to know the part of the sky the two objects traveled. At any time there are tens of satellites over any spot on Earth, so not having your orientation nor constellations as reference is very difficult to assert what you actually saw. You gave very very little information thus my answer has to rely in heavy assumptions:
I'm going to assume these coordinates 50°05'16"N 14°26'21"E, which correspond to the center of Prague.
I'm also going to assume both were satellites (it could have been a high altitude airplane by your description, or many other things).
I'm going to assume you and your friend did this observations with the naked eye and thus that the magnitude should be below 4 mag (since there are still tens of satellites from that location at that time that are in the 4 to 6 mag range).
And finally I'm also going to assume that the "around 19:30" means literally 19:30 (a difference in 5 minutes completely changes the entire set of satellites above your head so there has to be less than 1 minute uncertainty here).
In that case my best bet is that the first object was the SHIJIAN-16 2013-057A satellite, a Chinese satellite launched in 2013 and that happened to go across the Big Dipper at 19:30 from Prague with a visual brightness of 3.5 mag. Its purpouse is to probe the space environment, radiation and its effects, record space physical environment parameters, and conduct other related space experiments.
For the second observation I also agree that it was probably the ISS. But if you were watching to the NE instead of the SW then it might have been the SL-16 R/B 1994-074B rocket fuselage that remained on orbit after the deployment of the Russian RESURS O1 satellite in 1994, since the calculated brightness was 3.2 mag (perfectly visible even if not so impressive as the ISS).
But how do I find the first one? Is there some general online service (similar to the one linked above) that could help me to identify which flying object I saw (not just ISS)?
I used Heavensat and downloaded all the TLEs available from there. It's the best freely available software for this, as far as I am aware of.