Correct me if I'm wrong but I remember playing TR1 on my PS1 way back in the day and to save you had to activate certain crystals. I never played the PC version until now and it looks like it has a "save anywhere" feature similar to that of TR2.

Am I remembering the crystals wrong or is the PC version different in this way?

The Console version had limited saves using the "Save Crystals"; the PC version always had unlimited saves.

Only the Console Versions had Save Crystals