I thought this topic would be a relatively easy "define and go" type of post. Not so!
I thought it was going to be a simple doublet vs triplet distinction but it is not. I will now refer you to the "bible" on all matters optical -- Amateur Telescope Optics (ATO): https://www.telescope-optics.net/index.htm -- you should definitely bookmark this site if you haven't already done so.
Since we all know what an Achromatic objective is, I'll just start with what the ATO thinks an Apochromatic objective is:
- "Put simply, the term apochromatic specifically implies the mode of chromatic correction, not the level of optical quality. For that, we have and should use appropriate parameters from the realm of optical aberrations."
So now you are probably thinking, JT, I need more than this, I need greater depth to fully appreciate the difference. I understand, but for me to explain all that is involved is both long and complex, so here is the link to the Achromats, Semi-APO, and APO chapter of the ATO https://www.telescope-optics.net/apo_refractor.htm.
I must tell you that before you begin this section, you should go fetch a beverage and put on your thinking cap - you'll need it because MATH is involved!
You can thank me for your headache later.