For me, where there are 2 different materials meeting, I use caulk. The 2 materials expand and contract at DIFFERENT rates, hence, the use of caulk. Caulk will move. If you grout, it will most likely crack and separate, leading to worst problems. As for YOUR case, the porcelain and tile are almost the same material. So, it's a toss-up. BUT, I recommend you use caulk.
If you re-caulk, clean out the 'joint' as best you can. Then use a mild household cleaner to clean the area you're caulking. Yes, use a Tub and Tile Caulk. Fill the shower bottom with water (so it simulates a person in the shower), and caulk. Let it dry per the tube's specifications. For a nice bead, get a little container of slightly-soapy water. When you put on a bead of caulk, gently run your finger along the length of the caulked surface. Wipe the excess caulk on your finger into a paper towel or rag. You might want to experiment first. Take 2 pieces of wood where you can 'create' a corner. (YOu don't need to create the 'space' that's between the tile and the tub. Then, run a bead of caulk. Dip your finger into the slightly soapy water and run it along the caulk. See?!!
If you have any more ???s, post up. My best to ya and hope this helps.