In the One Punch Man manga it's mentioned that Psychos increased her powers by receiving those from a god. Is this god who gave powers to Psychos the same god who gave powers to Homeless Emperor?
Unknown within the webcomic or manga. Psykos has never mentioned any such being/encounter in the webcomic. She has said to Saitama and Fubuki that she knows of some terrifying truth about the future, which set her on the Monster Association path, but she has not been seen or heard since then in any form. And the manga hasn't revealed Homeless Emperor's connection beyond what the webcomic has provided (which isn't much).
There are some substantive differences in the portrayals in the two mediums. The being Psykos sees in the manga is basically just some some sort of spherical meat lump, which she describes as having endless swirls on its surface and resembles Jupiter, whereas Homeless Emperor's vision in the webcomic is of a (colossal) humanoid. He originally appears to Homeless Emperor as little more than a scribble of lines in human form. It's not until his demise that he sees his "god" in a more fleshy appearance. This second incarnation shares the same textural appearance as Psykos's, so it at least seems reasonable to suppose they are intended to be the same entity, or at least related ones. For what it's worth, the wiki considers them the same being.