The thanksgiving offering also differs in that it was to include three types of grain offering - unleavened bread, unleavened wafers, and loaves of (leavened) bread. In most mentions of leaven (yeast) in the bible, the context indicates that leaven represents sin, so why would the thanksgiving offering include a loaf of leavened bread?
First, because our thanks to God are not dependent on us being free of sin, a good thing, since we aren't. We don't give thanks because our lives are perfect, we give thanks because despite our sin, God accepts us. In the sacrificial system, that acceptance followed their sacrifices made to atone for sin, but for us today, Christ is the sacrifice and we can be thankful every day that our sin has been covered by Him.
Another distinction of this sacrifice is that it was brought, not by the priest, but by the individual. It was an offering that the person made to give thanks for all that God had done for them. And it was a sacrifice to be shared with the priest as well as with the one who brought it, magnifying the Lord by sharing what He has done with others.
After offering the sacrifice and waving the offering before the Lord as a visible way of expressing where these resources came from, the offerer and the priest would feast on them together to celebrate God's goodness. But the offering had to be entirely consumed in the day it was offered, none could be kept until the following day. The idea conveyed is that we should give thanks daily.
How often does God provide for us? Daily.
In fact, multiple times throughout each day. This is the origin for our "saying the blessing" or "giving thanks" before a meal -- that we should remind ourselves, and tell others around us, that God provided this meal for us and we are grateful not only for the meal but for all that He has given us.