A font that's a different type (OTF vs. TTF vs. Type 1) from the original will not be recognized as "the same" by an of the Adobe applications, even if the name is the same. If the name is the same but it's a different font from a different foundry, once again Photoshop will not agree that it's the same font. Even a different version of the same font will not be acknowledged.
The reason for this is that a different font file from the original can (and often will) cause text to reflow unexpectedly, which can be disastrous (consider a carefully set page layout where line breaks and spacing have been fine-tuned).
In your case, this may not be a big deal, so you can simply go into the Character Panel and change the layer font to the one you have installed. There may be a slight change in appearance, but you can adjust for it.